class11 physics sample paper

CLASSXI 

SAMPLE PAPER OF PHYSICS

SET-I

Sr No.		Marks
	Give dimensions of (i) rotational Kinetic energy (ii) strain.	1
	Why the wheels of automobiles are circular in shape.	1
	An electron and proton possess same momentum. Which one has lesser kinetic energy? OR A body of mass 100 kg falls from a height of 10 m. Find increase in kinetic energy .	1
	Name the physical quantity is represented by the product of moment of inertia and angular acceleration?	1
	An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0. What will be its potential energy?	1
	When does a body acquire a permanent set? OR Name the ratio of the change in dimension at right angles to the applied force to the initial dimension.	1 1
	Why hot soup tastes better than cold soup?	1
	The surface temperature of a hot body is 12270 C. Find the wavelength at which it radiates maximum energy. Given Wien’s constant = 0.2898CmK OR Why must telephone or power lines necessarily slag a little?	1
	State the law of equi-partition of energy?	1
	Glass windows may be broken by a faraway explosion. Explain why? OR Name the two important properties of a material medium responsible for the propagation of wave through it	1
	For question numbers 11, 12, 13 and 14, two statements are given-one labelled Assertion (A) and the other labeled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.  a) Both A and R are true and R is the correct explanation of A  b) Both A and R are true but R is NOT the correct explanation of A  c) A is true but R is false  d) A is false and R is also false
	Assertion      (A): Greater is the mass, greater is its inertia. Reason          (R): Mass of a body is measure of its inertia.	1
	Assertion     (A):   When a bullet is fired from a gun at rest, net finite momentum of bullet plus gun is non-zero. Reason        (R): Internal forces can cause change in linear momentum of the system.	1
	Assertion      (A): Use of ball bearings between two moving parts of machine is a common practice Reason          (R): Ball bearings reduce vibrations and provide good stability.	1
	Assertion       (A): When a lift is accelerated up, the net weight of a body increases. Reason        (R): When the lift is accelerated up, the pseudo forces acts on the body in downwards direction	1
	Section B Questions 15 and 16 are Case Study based questions and are compulsory. Attempt any 4 sub parts from each question. Each question carries 1 mark.
	Q.15 In daily life, a body is said to be elastic if a large deformation produced or strain is produced on applying given stress on it. In physics, elasticity is the property of the material of a body by virtue of which it opposes any change in its size or shape when stress is applied on it. Due to repeated stress and strain, spring of spring balance loses the elastic behavior. The spring of such a balance takes longer time to recover its original configuration. During long use, a bridge suffers alternating strains continuously. Consequently, the elastic strength of the bridge gets reduced. After a long time, the bridge develops elastic fatigue and therefore there occurs a permanent change in its structure. Elasticity means…………………………. a) Large deformation                                                 b) loss of strength          c) property of regaining the original shape               d) not regaining the shape A spring balance does not give correct reading when it has been used for a long time. a) Not branded                                                         b) due to elastic fatigue c) Rusting                                                                 d) made up of alloy Which is more elastic? a) Rubber                                                                 b) iron  c) Steel                                             d) none of these The bridges are declared unsafe after long use because--------- a) New one to build                                                b) it may collapse due to elastic fatigue c) old is gold so no need to build new                   d) due to increase in vehicles  Rubber is…………………………. a) Elastic                                                                b) plastic c) Elastomer                                                          d) none of these	4
	Q16. Any motion repeating over and over at regular intervals of time is called periodic motion. If it is back and forth as well, it is called vibratory or oscillatory or harmonic. Uniform circular motion is an example of simple harmonic motion. S. H. M can be represented by X= A sin (wt+ φ) or X=A cos (wt+ φ) or combination of both. If we take an example X= 10sin (20t+0.5), where displacement is measured in meters and time in seconds, we can find different parameters related to S. H.M just by comparing with the above equation. Simple harmonic motion is ……………………….  a) Periodic only                                                        b) Periodic as well as oscillatory c) Directed towards extreme position                      d) None of these In the above example the value of amplitude is …………. 10m                                                                                 b) 20m 30m                                                                                 d) Zero What is the value of frequency? 0.318Hz                                                                          b) 3.18Hz               c)  318Hz                                                                                   d) 20 rad/s The time period of the S.H.M is   a)  314s                                                                                       b)   3.14s         c) 0.314s                                                                                      d)   0.5 s  The phase difference between displacement and velocity for the given expression is: a) 00                                                                                            b) 1800  c) 900                                                                   d) 2700	4
	Section C All questions are compulsory. In case of internal choices, attempt anyone
	What is the percentage error in volume of a sphere, when error in measuring its radius is 2%?	2
	The position coordinate of a moving particle is given by x=6+18t+9t2  (x in meter, t in seconds) what is its velocity at t=2s	2
	Give two reasons to explain that static friction is a self-adjusting force. How much force of static friction is acting on the block of mass 2 kg shown in figure below if the coefficient of static friction between the block and the surface is 0.2?	2
	With suitable examples explain that work done may be zero and negative   OR Derive expression for loss in kinetic energy for completely inelastic collisions	2
	A body of weight 64N on the surface of earth. What is the gravitational force on it due to the earth, at a height equal to the half of the radius of earth? Acceleration due to gravity on the surface of the earth is 10ms-1. OR Find out expression for velocity required for an object to escape from surface of earth so that it never returns by its own.	2
	A flywheel of mass 25kg has a radius of 0.2m. What force should be applied tangentially to the rim of the flywheel so that it acquires an angular acceleration of 2 rad/s2?	2
	Show that the coefficient of areal expansion ‘β’ of a rectangular sheet of the solid is twice the coefficient of linear expansion ‘α’.	2
	What do you mean by degrees of freedom? Find the ratio of specific heats Cp / Cv for monatomic gas? OR  Define average speed, root mean square speed and most probable speeds. Express these speeds in terms of temperature of the gas	2
	Atmosphere is very thin at the Moon surface, why?	2
	Section D All questions are compulsory. In case of internal choices, attempt anyone
	A Body covers 12m in 2nd second and 20m in 4th second. How much distance will it cover in 4 second after the 5th second?	3
	Find an expression for the maximum speed with which a vehicle can safely negotiate a curved road banked at angle θ the coefficient of friction between the wheel and the road is μ	3
	A body whose moment of inertia is 3 Kg-m2 is at rest it is rotated for 20 s with moment of force of 6 Nm .Calculate  (i)  the angular displacement of the body and (ii) the work done	3
	State and prove work-energy theorem.    OR Define conservative and non-conservative force. Give one example of each.	3
	In fig. an ideal gas changes its state from A to C by two paths ABC & AC OR Derive an expression for work done during an adiabatic process. Show that the slope in adiabatic process is ϒ times the slope in isothermal process.	3
	Section E All questions are compulsory. In case of internal choices, attempt anyone
	Derive an expression for energy of a particle executing simple harmonic motion. If the displacement of two particle executing simple harmonic motion are represented by equations y1 = 4 sin (10t+π/3) and y2=5 cos10t, then what is the phase different between the  velocities of these particle?                                                                                               OR     What do you mean by a progressive wave? Derive an equation for progressive wave travelling along +ve X- direction. What would be the amplitude, wavelength and velocity of the wave represented by   φ (x,t) = 5sin(6π t - 4x) where ‘x’ the distance and ‘t’ the times are in SI units?	5
	A liquid in streamline flow through a tube of non uniform cross section then prove that sum     of its kinetic energy pressure energy and potential energy per unit volume is constant.  Write down two limitations of this principle.  Write its two applications of the same.                                                        OR   With the help of appropriate diagram show that maximum constant velocity acquired by a body while falling freely through viscous medium is given by   29r2(ρ-σ)g. Where symbols have their usual meanings. Why object acquire this velocity and  also write its specific name.	5
	33 A car accelerates from rest at a constant rate of α for some time, after which it decelerates at a constant rate β to come to rest. If the t is total time elapsed, then calculate The maximum velocity attained, and Total distance travelled by the car Average velocity                                                          OR    If a body is projected with some initial velocity making an angle θ with the horizontal, show that   its path is a parabola. Then find,   a) The maximum height attained   b) The time of flight   c) Horizontal range   d)Maximum horizontal range	5

COMMON SESSION ENDING EXAMINATION 2020-21

SUBJECT : PHYSICS (ANSWER KEY)

SECTION A
Direction (Q-1 to 14) Select the most appropriate option
1		Ans1. (i) [M L2 T-2]  (ii) Dimensionless	12+12
2		Rolling friction less than sliding friction	1
3		Proton                    Or  9800J	1
4		Torque	1
5		2E0	1
6		When load is applied beyond elastic limit                                 Or  Lateral strain	1
7		Low surface tension	1
8		λm=b/T, =19320A0                       Or In winters the wires contract and may become too tight to bre	1
9		Correct statement	1
10		Because it will vibrate with the frequency of forced oscillations               and as glass is brittle, it may break.                                               Or Elasticity and inertia	1
11		a	1
12		d	1
13		c	1
14		a	1
		SECTION-B
15		i. (c)        ii.  (b)        iii. (c)        iv.  (b)         v.  (c)	1+1+1+1
16		.i. (b)      ii.  (a)        iii. (b)        iv.  (c)         v.  (c)	1+1+1+1
SECTION-C
17	ɅV/Vx100% =3Ʌr/r x 100%=3x2= 6% formula and calculation		1+1
18	Velocity= 18+18t=54m/s velocity and result		1+1
19	Us = fs/R, R=mg    = 3.92N
20	Two examples Or Derivation		1+1
21	. Weight of body =mg=64N=mg=64N           ∴mass of body, m=64/g=64/10=6.4kg. At height h, the value of g' is given by, g'=g.R2/(R+h)2=10R2/(R+R/2)2=10×4/9 ∴∴ Weight at a height h=mg'=6.4×10×4/9 =28.44N                Or  Derivation & diagram		2 112+12
22	. I= 12MR2 =0.5kgm2 ,Ʈ=F.R=Iɑ=5N		1+1
23	Derivation of relation
24	Statement, CP/CV= 1.66                                                                                       Or  Definitions & writing formulae		12+112                                                                 112+12
25	Low value of escape velocity as compared to thermal speed		2
	Section-D
26	. Finding acceleration and initial velocity &S9-S5 a=4m/s2&u=6m/s ,S9-S5=136m		1+1+1
27	Correct expression		3
28	θ=400rad  W=2400J		2 1
29	Statement & derivation                 Or Definition & example of each		1+2
30	Wabc=60J, WAC=40J 1+1+1 UC=170J ɅQ= ɅUAB +ɅWAB=UB-UA+ɅWAB =20-10+0=10J or Derivation and (slope)adi=ϒ(slope)iso		112+ 112 2+1
	SECTION-E
31	Derivation , numerical correct answer= ɸ1- ɸ2= - π/6                                          OR Statement, equation & answers for amplitude, wavelength & velocity		3+1+1 1+1+1+1+1
32	Derivations , Applications, Limitations OR Derivation, diagram + explanation and name.		3+1+1 (3+12)+112
33	calculations, exact answers i) vmax= αβα+βt   ii)     12αβα+βt2       iii) vav = 12αβα+βt                                              OR Proof of path,& other parts		2+2+1 1 +1+1+1+1

PHYSICS SAMPLE PAPER 

SET-II

Common Session Ending Examination 2021
SECTION - A
Sr. No.	All questions are compulsory. In case of internal choices, you can attempt any one of them.			Marks
1.	Why are freely falling rain drops spherical in shape? Give reason.			1
2.	The stress strain graphs for two materials A and B are shown in figure. Which material is more brittle and why?			1
3.	Define Wien’s Displacement Law. Write the SI unit of Wien’s constant. OR At which temperature water has maximum density?			1
4.	A body falling from a height of 10 m rebounds from a hard floor. It loses 20 % of its energy in the impact. What is the height to which it would rise after the impact?			1
5.	How will the time period of a simple pendulum change if its length is doubled? OR All oscillatory motions are periodic but all periodic motions are not oscillatory. Comment on it with suitable example.			1
6.	The temperature (in Kelvin) of the gas is increased 4 times. What will be the increase in root mean square velocity of the gas molecule?			1
7.	If x=at+bt2, where x is in metre and t is in second then find the dimensions of a and b.			1
8.	Write two methods of reducing force of friction. OR A force of 5 N is acting on the object of mass 1 Kg which is moving with uniform velocity. What is the force of friction acting on the object			1
9.	When the earth shrinks without reducing its mass, what change will be there in the duration of a day and why? OR The speed of the inner layers of the whirl wind in a tornado is alarmingly high. Why?			1
10.	The mass of two bodies are doubled and distance between them is halved, how will the gravitational force change with respect to its initial value?			1
	For question numbers 11, 12, 13 and 14, two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is NOT the correct explanation of A. (c) A is true but R is false. (d) A is false and R is also false.
11.	Assertion (A): A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table. Reason (R): For every action, there is an equal and opposite reaction.			1
12.	Assertion (A): On a rainy day, it is difficult to drive a car or a bike at high speed. Reason (R): The value of coefficient of friction is lowered due to wetting of the surface.			1
13.	Assertion (A): Centripetal force is directed tangentially to the motion of the object in circle Reason (R): Centripetal force is directly proportional to the radius of the circular path.			1
14.	Assertion (A): It is easier to pull a heavy object than to push it on a level ground. Reason (R): The magnitude of frictional force depends on the nature of the two surfaces in contact.			1
	Section – B Questions 15 and 16 are Case Study based questions and are compulsory. Attempt any 4 sub parts from each question. Each question carries 1 mark.
15.	When a force is applied on body, it is deformed. In the case of a wire, suspended from ceiling and stretched under the action of a weight (F) suspended from its other end, the force exerted by the ceiling on it is equal and opposite to the weight. However, the tension at any cross-section A of the wire is just F and not 2F. Hence, tensile stress which is equal to the tension per unit area is equal to F/A. Hooke’s law is valid only in the linear part of stress-strain curve. Young’s modulus and shear modulus are relevant only for solids since only solids have lengths and shapes. Bulk modulus is relevant for solids, liquid and gases. It refers to the change in volume when every part of the body is under the uniform stress so that the shape of the body remains unchanged. Metals have larger values of Young’s modulus than alloys and elastomers. A material with large value of Young’s modulus requires a large force to produce small changes in its length. The material which stretches to a lesser extent for a given load is considered to be more elastic. In general, a deforming force in one direction can produce strains in other directions also. The proportionality between stress and strain in such situations cannot be described by just one elastic constant. (i) Young’s modulus of a substance depends upon: (a) Its length                                                       (b) Its area (c ) Acceleration due to gravity                         (d) None of the above (ii) The value of Young’s modulus for a perfectly rigid body is: (a) Infinity                                                          (b) Zero (c ) One                                                              (d) None of the above (iii) If the temperature of a wire is doubled, the Young’s modulus of elasticity: (a) Increase                   (b) No change               (c) Decrease (d) May increase or decrease depending upon the thickness of the material. (iv) Young’s modulus is numerically equal to the stress that arises in a wire when its length L changes to: (a) 1.25 L       (b) 1.50 L       (c) 2.00 L      (d) Remain same (L) (v) The value of Bulk modulus for an ideal fluid is: (a) Infinity      (b) Zero         (c) One         (d) None of the above			4
16.	The period T is the least time after which motion repeats itself. Thus, motion repeats itself after nT where n is an integer. Every periodic motion is not simple harmonic motion. Only that periodic motion governed by the force law F = – k x is simple harmonic. The constant of proportionality k is called the spring constant, its value is governed by the elastic properties of the spring. A stiff spring has large k and a soft spring has small k. Circular motion can arise due to an inverse-square law force (as in planetary motion) as well as due to simple harmonic force in two dimensions equal to –mω2r. A combination of two simple harmonic motions with arbitrary amplitudes and phases is not necessarily periodic. It is periodic only if frequency of one motion is an integral multiple of the other’s frequency. However, a periodic motion can always be expressed as a sum of infinite number of harmonic motions with appropriate amplitudes. The period of SHM does not depend on amplitude or energy or the phase constant. The total mechanical energy of a harmonic oscillator is independent of time as expected for motion under any conservative force. The motion of a simple pendulum is simple harmonic for small angular displacement. (i) A particle performing simple harmonic motion starts from mean position. The phase of that particle is π/2 when it has: (a) Maximum displacement                             (b) Maximum velocity  (c) Maximum energy                                       (d) Maximum kinetic energy (ii) A spring of force constant k is cut into two parts such that one piece is double the length of the other piece. Then the long piece will have a force constant of: (a) 2k/3                            (b) 3k/2                    (c) 3k                   (d) 6k (iii) The frequency of total energy of a particle in simple harmonic motion is: (a) Infinity                       (b) Zero                   (c) One                 (d) 10 (iv) A 5 kg collar is attached to a spring of spring constant 500 N m–1. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10.0 cm and released. Calculate the period of oscillation. (a) π                                 (b) π/2                      (c) π/5                   (d) 2π/3  (v) What is the length of a simple pendulum, which ticks seconds? (a) 1 m                            (b) 2 m                     (c) Infinite             (d) 1 cm			4
17.	Section – C (i) There are two specific heats of a gas; specific heat at constant pressure and specific heat at constant volume (CP & CV). Why? (ii) Which one of them is greater and why?			2
18.	Two masses m and 4m are placed at a distance d from each other. Where should a mass m0 be placed on the line joining theses masses, so that the net force acting on m0 is zero? OR The escape velocity of a projectile on the Earth’s surface is 11.2 km/s. A body is projected out with twice this speed. What is the speed of the body far away from the Earth, i.e., at infinity? Ignore the presence of the Sun and other planets etc.			2
19.	Derive an expression for the orbital velocity of a satellite.			2
20.	Each side of a cube is measured to be 7.2 m. What are the total surface area and the volume of the cube to appropriate significant figures? OR A physical quantity P is related to four observables a, b, c and d as follows: P= a3b2c d, The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P?			2
21.	Draw velocity vs time graph for uniformly accelerated motion. What is its graphical importance?			2
22.	(i) Define torque or moment of force. (ii) Why we cannot open or close a door by applying force at the hinges?			2
23.	State and prove work energy theorem.			2
24.	What is the mean free path? Write its expression. On what factors does the mean free path depend? OR State the law of equi-partition of energy and apply it to find the specific heat capacities (Cp and Cv) of diatomic gas.			2
25.	Derive an expression for maximum velocity of a car moving on a banked circular road having coefficient of friction µ.			2
26.	Section – D Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3 kg.			3
27.	Define isothermal process. Derive an expression for work done during isothermal process.			3
28.	(i) Differentiate uniform and non uniform motion. (ii) A car moving along a straight highway with speed of 126 km h–1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop? OR A player throws a ball upwards with an initial speed of 29.4 m s–1. (i) What is the direction of acceleration during the upward motion of the ball? (ii) What are the velocity and acceleration of the ball at the highest point of its motion? (iii) To what height does the ball rise? (Take g = 9.8 m s–2 and neglect air resistance).			3
29.	(i) What is centripetal force?  (ii) Derive an expression of Centripetal acceleration			3
30.	State if each of the following statements is true or false. Give reasons. (i) In an elastic collision of two bodies, the momentum and energy of each body is conserved. (ii) Work done in the motion of a body over a closed loop is zero for every force in nature. (iii) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system. OR (i) Define power. Write its expression and SI unit. (ii) A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. Find the power delivered to it in terms of time t.			3
31.	Section – E (i) What are progressive waves? How are they different from stationary waves (any three differences)? (ii) A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36 t + 0.018 x + π/4) where x and y are in cm and t in s. The positive direction of x is from left to right. (a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation? (b) What are its amplitude and frequency? (c) What is the initial phase at the origin? OR (i) What are beats? How are they produced? What should be the difference between the frequencies to produce beats and why? (ii) Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B if the frequency of A is 427 Hz?			5
32.	(i) State parallelogram law of vector addition. Derive the expression for the magnitude and direction of a resultant vector by using this law. (ii) What is the basic condition for the composition of vectors? (iii) Find the rectangular components of a force of 10 N if it makes an angle 300 with the horizontal direction. OR (i) A body of mass m is fired with a velocity u making an angle θ with the horizontal. Derive expressions for time of flight & horizontal range. (ii) What is the condition to get maximum range? (iii) Prove that horizontal range will be same for two angles of projection whose sum is 900.			5
33.	(i) State and prove Bernoulli’s theorem for a liquid having streamline flow. (ii) A pipe is running full of water. At a certain point A, it tapers from 60 cm diameter to 20 cm diameter at B. The pressure difference between A and B is 100 cm of water column. Find the speed of water through the pipe at end A.  OR (i) Explain the principle on which hydraulic lift works. (ii) In a car lift compressed air exerts a force F1 on a small piston having a radius of 5.0 cm. This pressure is transmitted to a second piston of radius 15 cm. If the mass of the car to be lifted is 1350 kg, calculate F1. What is the pressure necessary to accomplish this task? (g = 9.8 ms-2). (iii) What is the pressure on a swimmer 10 m below the surface of a lake?			5

                       ANSWER KEY 

SET-II

Common Session Ending Examination 2021
XI Physics (ANSWER KEY)
1.	Due to surface tension. The drops try to occupy minimum surface area, and for a given volume sphere has minimum surface area.	1
2.	Material B is brittle.                                  ½ mark Because it has less plastic region.             ½ mark	1
3.	Wien’s Displacement Law: Wavelength λm decreases with an increase in temperature. λm α 1/T       OR    λm T = b (Wien’s constant).               ½ mark SI unit of Wien’s constant (b): mK                                                      ½ mark OR 40C.                   1 mark.	1
4.		1
5.	For a simple pendulum, T = 2πlg          ½  mark T' =  2πl'g   =  2π2 lg  =  2 T               ½ mark                         OR All oscillatory motions are periodic but all periodic motions are not oscillatory. For example, motion of moon around earth is periodic but not oscillatory. 1 mark	1
6.	As vrms ∞ T so Vrms becomes double.	1
7.	Dimension of a = [M0LT-1]              ½ mark Dimension of b = [M0LT-2]              ½ mark	1
8.	Two methods     ½  mark each OR 5 N                      ½  Mark Reason                ½ mark	1
9.	As angular momentum L is conserved. If Earth shrinks, r will decrease moment of inertia I will decrease and angular velocity will increase. So duration of the day will decrease.    1 mark                  OR The speed of the inner layers of the whirl wind in a tornado is alarmingly high. L = I ω = constant. If I will decrease, ω will increase.       1 mark	1
10.	16 times more      1 mark
11.	(b)	1
12.	(a)	1
13.	(d)	1
14.	(b)	1
15.	(i) (d) None of the above (ii) (a) Infinity (iii) (c) Decrease (Y = Thermal stress / α ∆T) (iv) (c) 2.00 L (v) (a) Infinity	1 mark  Each part
16.	(i) (a) Maximum displacement (ii) (b) 3k/2                     (iii) (b) Zero                    (iv) (c) π/5                           (v) (a) 1 m	1 mark  Each part
17.	(i) Correct reason: 1 mark (ii) CP  > CV         ½ mark,     Reason: ½ mark	2
18.	Formula      ½ marks Calculation x=d/3         1½  marks OR 12 mv'2 = 12 mv2 - 12mve2                               1 mark v' = v2- ve2 = (2ve)2- ve2                ½ mark =  3ve = 1.732 X 11.2 km/s = 19.4 km/s   ½ mark	2
19.	Diagram: ½ mark, Derivation: 1.5 marks	2
20.	Total surface area = 6l2 = 6 (7.2)2 = 311.04 m2 ≈ 310 m2 (appropriate significant figures).                   1 mark Volume of the cube = (side)3 = (7.2)3 =  373.248 m3 ≈ 370 m3 (appropriate significant figures). 1 mark OR Correct formula: 1 mark, Correct application of values & answer: 1 mark	2
21.	Correct graph: 1 mark  Importance:    1 mark 1. Slope of graph is used to find acceleration. 2. Area under velocity time graph with time axis is equal to displacement.	2
22.	(i) Definition of torque or moment of force: 1 mark (ii) τ=r×F×sinθ, If r=0, τ=0         1 mark	2
23.	Statement: ½ mark,  Proof: 1.5 marks	2
24.	Definition of mean free path:              ½ mark Expression: λ=kBT2d2P=m2d2       ½ mark Factors on which the mean free path depend: temperature, diameter, pressure, density & number of molecules per unit volume. 1 mark OR Statement       ½  mark Derivation of Cv =5/2 R and Cp= 7/2 R                            1 ½  marks	2
25.	Diagram: ½ mark, Derivation: 1.5 marks	2
26.	L-shape consists of 3 squares each of length 1m & mass 1kg. The centres of mass C1, C2 and C3 of the squares are, by symmetry, their geometric centres and have coordinates (1/2,1/2), (3/2,1/2), (1/2,3/2) respectively.    1 mark We take the masses of the squares to be concentrated at these points. The centre of mass of the whole L shape (X, Y) is the centre of mass of these mass points. Formulae of X & Y:     1 mark X = 5/6 m, Y = 5/6 m   1 mark	3
27.	Definition of isothermal process: 1 mark Derivation for work done during isothermal process: 2 marks	3
28.	(i) Differentiate uniform and non uniform motion: 1 mark (ii) u = 126 km h–1 = 35 ms-1, a = -3.06 ms-2,      Retardation = 3.06 ms-2                                      2 marks OR (i) Vertically downwards:                                     1 mark (ii) v = 0, a = g = 9.8 ms-2 vertically downwards: 1 mark     (iii) v2 – u2 = 2as, s = h = - 44.1 m                        1 mark	3
29.	(i) Definition             1 mark (ii) Derivation            2 marks	3
30.	(i) False ½ mark, Reason: ½ mark (ii) False ½ mark, Reason: ½ mark (iii) True ½ mark, Reason: ½ mark OR (i) Power: The time rate of doing work is power. ½ mark     P = W/t and SI unit is watt (W).                       ½ mark (ii) u = 0, v = u + at = at, P = Fv = ma2t               2 marks	3
31.	(i) Progressive waves (definition): ½ mark, Three differences: 1.5 marks (a) Travelling wave propagating right to left as x is +ve.                          ½ mark Speed = wavelength / Time period = 20 ms-1.                                          ½ mark Direction of its propagation = Propagating right to left as x is +ve.         ½ mark (b) Amplitude = 3 cm                                       ½ mark Frequency = 1/T = 5.73 Hz                              ½ mark (c) Initial phase at the origin: ϕ = π/4 rad        ½ mark OR (i) Beats (Definition): 1 mark, Production: 1 mark Difference between the frequencies to produce beats: Less than 10        ½ mark Reason: ½ mark (ii) Increase in the tension of a string increases its frequency. If original frequency of B (νB) were greater than that of A (νA), further increase in νB should have resulted in an increase in the beat frequency. But beat frequency is found to decrease. This shows that νB < νA. Since νA – νB = 5 Hz, and νA = 427 Hz, we get νB = 422 Hz.              2 marks	5
32.	(i) Statement: 1 mark, Diagram: ½ mark, Derivation of magnitude: 1 mark Direction: ½ mark (ii) Basic condition for the composition of vectors: Vectors of same nature can be added only. We cannot add force into momentum. 1 mark (iii) F = 10 N, Fx = 10 cos 300 = 53 N          ½ mark                        Fy = 10 sin 300 = 5 N                ½  mark OR (i) Diagram: ½ mark, Derivation of time of flight: 1 mark & horizontal range: 1 mark. (ii) To get maximum range, projectile must be fired at an angle of 450.   ½ mark (iii) Proof: 2 marks	5
33.	(i) Statement: ½ mark, Diagram: ½ mark, Proof of Bernoulli’s theorem: 2 marks  (ii) V  = A1v1 = A2v2,                                               ½ mark π x (30)2v1 = π x (10)2v2 or v2 = 9v1                       ½ mark Further, as P1 + 12v12 = P2 + 12v22,   12 (v22 - v12) = (P1-P2)       ½ mark Or  12 (81 v12 - v12) = 100 cm of water column v1 = 100 x 1 x 98040 cm/s = 35 2 cm/s                                        ½ mark OR (i) Principle of hydraulic lift (Pascal’s Law): It states that in an enclosed fluid, if pressure is increased at any one part of the fluid then it is equally transmitted to all other parts (pressure to all parts will be same). If area will increase then force will also increase. If area will decease then force will also decrease.                1 mark (ii) F1 = F2 X A1 / A2 = 1470 N                                     1 mark Pressure necessary = P = F1 / A1 = 1.9 X 105 Pa            1 mark (iii) Pressure on a swimmer P = Pa + ρgh                        1 mark = 1.01×105 Pa + 1000 kg m–3 ×10 m s–2 ×10 m = 2.01 × 105 Pa ≈ 2 atm    1 mark	5

COMMON SESSION ENDING EXAMINATION 2021

CLASS: XI                                                                                                        MM: 70

SUB: PHYSICS 

SET-III                                                                                              TIME: 3hrs.

General Instructions:

(1) All questions are compulsory. There are 33 questions in all. 

(2) This question paper has five sections: Section A, Section B, Section C, Section D and      Section E. 

(3) Section A contains ten very short answer questions and four assertion reasoning MCQs of 1 mark each, Section B has two case based questions of 4 marks each, Section C contains nine short answer questions of 2 marks each, Section D contains five short answer questions of 3 marks each and Section E contains three long answer questions of 5 marks each. 

(4) There is no overall choice. However internal choice is provided. You have to attempt only one of the choices in such questions.

SECTION A

1. The error in the measurement of radius of a sphere is 2%. Find the % error in the measurement of volume.

2. What is the unit of coefficient of limiting friction?

3. How will the time period of simple pendulum change when its length is doubled?

4. Why we place handles at maximum distance from the hinge in a door?

OR

What is analogy of force in angular motion?

5. What would happen to an orbiting planet if gravitational forces ceases to act on it.

6. Define Bulk modulus of elasticity?

OR

Which is more elastic; rubber or steel. Why?

7. Two soap bubbles have radius R and 2R respectively. Which of the two has greater excess pressure?

OR

How angle of contact varies with temperature?

8. Two stars radiate maximum energy at wavelength 3.6 x 10-7 m and 4.8 x 10-7 m respectively. What is the ratio of their surface temperature?

9. Define law of equipartition of energy?

OR

What is the no. of degree of freedom of non-linear (rigid rotator) triatomic molecule?

10. A simple pendulum is mounted inside a spacecraft. What should be its time period of oscillation?

For question numbers 11, 12, 13 and 14, two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

a) Both A and R are true and R is the correct explanation of A 

b) Both A and R are true but R is NOT the correct explanation of A 

c) A is true but R is false 

d) A is false and R is also false

    11. Assertion : A rocket moves forward by pushing the surrounding air backwards.
          Reason    : It derives the necessary thrust to move forward according to Newton’s   

                            Third law of motion.

 

12. Assertion:  Inertia is the property by virtue of which the body is unable to change by itself, its    

                   state of rest or motion and its direction of motion.

          Reason    : The bodies do not change their state unless acted upon by an unbalanced external   

                                 Force. 

     

      13. Assertion (A) : Newton's laws can be applied to bigger bodies
            Reason (R) : During any kind of collision the centre of mass of the system is not accelerated.

 

       14. Assertion (A): The acceleration produced by a force in the motion of a body depends       

                                     Only upon its mass.
          Reason (R):  Larger is the mass of the body, lesser will be the acceleration produced.

    

Section – B

Questions 15 and 16 are Case Study based questions and are compulsory. Attempt any 4 sub parts from each question. Each sub-part carries 1 mark.

 

15.  Young's Modulus Experiment: A typical experimental arrangement to determine the Young's modulus of a material of wire under tension is shown in figure. It consists of two long straight wires of same length and equal radii suspended side-by-side from a fixed rigid support. The wire A (called the reference wire) carries a millimetre main scale M and a pan to place a weight

 

The wire B (called the experimental wire) of uniform area of cross-section also carries a pan in which known weights can be placed, vernier scale is attached to a pointer at the bottom of experimental wire B and main scale is fixed to the reference wire A.

(i) When a weight is placed in the pan, which type of stress is produced in it,

           (a) Tensile                                                     (b) Tangential

           (c) Bulk                                                         (d) Compressive

(ii)The reference wire is used to compensate for any change in length due to change in

(a) length of experimental wire                    (b) volume of experimental wire

(c) room temperature                                    (d) weight of pan

(iii) The difference between which two readings gives the elongation produced in the wire.

(a) Main                                                        (b) Vernier

(c) Reference                                                (d) Original wire

(iv) Suppose M be the mass of wire that produced an elongation ΔL in the wire, then the applied force is equal to

(a) Mg                                                          (b) Ma

(c) Mv                                                          (d) Mv2

(v) The Young's modulus of experimental wire is

(a) Mg x L/ (πr2ΔL)                                    (b) Mg x (πr2ΔL)/L

(c) (πr2ΔL)/ Mg x L                                    (d) Mg x πr2L/(ΔL)2 

16. P.E. of spring:

There are many types of spring. Important among these are helical and spiral springs. Usually, we assume that the springs are massless. Therefore, work done is stored in the spring in the form of elastic potential energy of the spring. Thus, potential energy of a spring is the energy associated with the state of compression or expansion of an elastic spring.

(i) The potential energy of a body is increases in which of the following cases

(a) If work is done by conservative force      

(b) If work is done against conservative force

(c) If work is done by non-conservative force

(d) If work is done against non-conservative force

(ii) The potential energy, i,e. U(x) can be assumed zero when

(a) x = 0                                                                       (b) Gravitational force is zero

(c) Infinite distance from the gravitational Source      (d) All of the above

(iii) The ratio of spring constants of two springs is 2:3. What is the ratio of their potential energy, if they are stretched by the same force?

1.  2:3            (b) 3:2          (c) 4:9        d) 9:4

(iv) The potential energy of a spring increases by 15 J when stretched by 3 cm. If it is  stretched by 4 cm, the increase in potential energy is

(a) 80/3 J                                      (b) 30 J

c) 33J                                           (d) 36 J

(v)  The potential energy of a spring when stretched through a distance X is 10J. What is the amount of work done on the same spring to stretch it through an additional distance x?

(a) 10 J                                               (b) 20 J 

(c) 30J                                                (d) 40J

SECTION – C

Q.17 If Length, Time and Energy are fundamentals units, find the dimensions of mass.

Q.18 State in the following cases,whether the motion is one,two or three dimensional

i) A kite flying on a windy day

ii) a speeding car on a long straight highway

iii) an insect crawling on a globe

iv) a planet revolving around its star.

Q.19 Why are mountain roads generally made winding upwards rather than going straight  

          up?

                                                               OR

         State the laws of static friction.

Q.20 State and prove work energy theorem for variable force.

                                                              OR

         An elastic spring of spring constant ‘k’ is compressed by an amount x. Show that its   

          potential energy is ½ kx2.

Q.21 Two solid spheres of the same mass are made of metals of different densities, which of 

          them has large moment of inertia? Why?

Q.22 Does the escape velocity of a body from the earth depends on: 

         a) the mass of the body b) the location from where it is projected? Explain your answer.

Q23.For a satellite orbiting in an orbit, close to the surface of earth, what is the percentage  

increase in the kinetic energy required so that it will escape the Earth’s Gravitational   pull.

                                                           OR

        If the radius of earth were increased by a factor of 3, by what factor its density have to 

         be changed to keep ‘g’ the same?

Q24 Explain why 

1. A body with large reflectivity is a poor emitter?

2. A brass tumbler feels much colder than a wooden tray?

Q.25 Explain the concept of absolute zero of temperature on the basis of kinetic theory of 

          gases.

 

SECTION – D

Q.26 A body cover 12m in 2nd second and 20m in 4th second. Find what distance the body     

         will cover in 4 seconds after the 5th second.

OR

 If x,y ,z be the distances described by a particle during the pth,qth and rth second     respectively prove that :  (q-r)x+(r-p)y+(p-q)z=0

Q.27 Define angle of friction and angle of repose. Establish a relation between them.

OR

         Find the expression of maximum velocity of vehicle on flat curved road.

Q.28 Show that for a particle in linear SHM, the average kinetic energy over a period of oscillation is equal to average potential energy over the same period.

Q.29 Obtain the expression of position of centre of mass of two particle system.

Q.30 Define adiabatic process. Derive an expression for work done during adiabatic process.  

  

SECTION- E

Q.31 (a) State parallelogram law of vector addition. Derive the formula for magnitude and   direction of the resultant.

(b) Two equal forces act at a point. The square of their resultant is 3 times of their Product. What is the angle between them?

                                                          OR

1.  A body is projected at an angle θ with the horizontal. Obtain expressions for its     

       maximum height, time of flight and horizontal range.

         (b) At what angle do the forces P+Q and P-Q acts such that the resultant is (3P2+Q2)1/2.

Q.32 (a) Prove that the sum of pressure, kinetic energy per unit volume and potential energy per unit volume is always constant for an ideal fluid having stream line flow.

(b) Water enters a horizontal pipe of non-uniform cross section with a velocity of        0.6ms-1 and leaves the other end with a velocity of 0.4ms-1. At the first end, the               pressure of water is 1200Nm-2. Calculate the pressure of water at the other end. Use Density of water as 1000kgm-3.

                                                                           OR

       (a) What is the phenomenon of capillarity? Derive an expression for the rise of liquid in a capillary tube of uniform diameter.

      (b) Water rises in a capillary tube to a height 2.0cm. i) In another capillary whose radius is one third of it, how much water will rise? ii) If first capillary is inclined to an angle of 600 with the vertical, then what will be the position of water in the tube?

Q.33(a) What are beats? Prove that number of beats per second produced by two sound sources are equal to difference between their frequencies.

(b) Calculate the number of beats per seconds produced by two waves 

    y1= 2sin(1000πt), y2= 2sin(988πt)

OR

For a travelling harmonic wave, y(x, t) = 2.0 cos2π(10t-0.0080x +0.35) where x and y are in cm and t is in seconds. What is phase difference between oscillatory motion of two points separated by a distance of (i) 4 m (ii) 0.5 m (iii) λ/2 (iv)

ANSWER KEY

SET-III

	answer	Marks distribution
1	6%, calculation using error equation	1
2	No unit	1
3	2 times the original time period	1
4	Correct explanation	1
	Or torque	1
5	The planet will fly tangent to its orbit into outer space	1
6	Correct def. or correct explanation	1
	Or correct explanation	1
7	p=4S/R, soap bubble with smaller radius have greater excess pressure	1
	Or increases	1
8	α1/T, 4:3	1
9	Correct definition	1
	Or 6
10	Infinity	1
11	A	1
12	A	1
13	B	1
14	B	1
15   (i)	A	1
(ii)	C	1
(iii)	B	1
(iv)	A	1
(v)	A	1
16   (i)	B	1
(ii)	D	1
(iii)	B	1
(iv)	A	1
(v)	C	1
17	Correct answer	2
18	Correct answer	½ mark each
19	Correct reason	2
	Or correct graph (1)  correct explanation (1)	2
20	Correct statement(1) correct proof(1)	2
	Or correct explanation	2
21	Moment of inertia of sphere with lesser density is more. Correct explanation	2
22	correct explanation	2
23	((Ve- V0)/ V0)x100 = 41.4%	2
	Or density reduces to 1/3 times the original value	2
24	Correct explanation(1+1)	2
25	Correct explanation	2
26	136 m	3
	OR correct expression	3
27	Definition (1/2 +1/2) relation (2)	3
	Or correct expression	3
28	Correct proof	3
29	Correct derivation	3
30	Correct derivation	3
31	(a)  statement +derivation                     1+2       (b)  formula+calculation(angle = 600)    1+1	5
	Or    Maximum height                                      1          Time of flight                                           1        Horizontal range                                       1        Formula + calculation (angle=  600  )     2	5
32	(a)    Derivation     3  (b)  Formula +calculation(P =1300Nm-2)     1+1	5
	Definition +Derivation                                                                                                          ½+2½   (b)Correct formula+calculation(i) height= 6cm,        ii) height h = 4.0cm)                                                                         1+1	5
33(a)	Definition (1) , derivation (3)	4
(b)	6 beats per second	1
	Or   camparision with standard equation (1), (i)6.4π radian    (ii)0.8 π radian (iii) π radian (iv) 1.5 π radian (each part I mark)	1+4

SAMPLE PAPER OF PHYSICS

SET-IV

Section - A

All questions are compulsory. In case of internal choices, attempt any one of them.

1. Find the dimensions of  b  in the equation P =a-t3b x where P is pressure, x is distance and t is time.

2. A horizontal force of 10N is necessary to just hold a block stationary against a wall. The coefficient 

of friction between the block and the wall is 0.2. What is the weight of the block?

3. Which is greatest out of static friction, limiting friction and kinetic friction?

4. A person sitting firmly over a rotating stool has his arms stretched. If he folds his arms, will there be any change in his angular momentum about the axis of rotation?

OR

A man carrying heavy weights in his hands and standing on a rotating turn table. If he draws his hands to his chest, how his angular speed will be affected?

5. What is the value of gravitational potential at infinity?

6. What force is required to stretch a copper wire 1 cm2in cross section to double its length? Y for copper is 1.26x1012 dyne cm-2

7. The ratio of radius of two soap bubbles of same soap solution is 2:1. What is the ratio of excess pressure inside them?

OR

An object is dropped from rest in a viscous medium. Plot a graph which shows the variation of velocity with time.

8. If the temperature of a perfectly black body is increased from 300 K to 900 K, by what factor the rate of emission will increase?

OR

Why clock pendulums are made up of invar?

9. A flask contains oxygen and hydrogen in the ratio 2:1 by mass at 27oC. Find the ratio of the average kinetic energy per molecule.

10. A child is swinging on a swing in the sitting position. How will the time period of the swing change if he stands up?

Assertion Reasoning based questions :

For question numbers 11, 12, 13 and 14, two statements are given-one labelled Assertion

1. and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below. 

a) Both A and R are true and R is the correct explanation of A 

b) Both A and R are true but R is NOT the correct explanation of A 

c) A is true but R is false 

d) A is false and R is also false

11. Assertion(A): It is easier to pull a heavy object than to push it on a level ground.

      Reason(R): The magnitude of frictional force depends on the nature of two surfaces in contact.

12. Assertion (A): A body can be at rest even when it is under the action of any number of external forces.

      Reason(R): Vector sum of all the external forces is zero.

13. Assertion (A) It is difficult to move a cycle along the road with its brakes on.

      Reason(R): Sliding friction is greater than rolling friction.

      14. Assertion(A): A horse has to pull a cart harder during the first few steps of his motion.

            Reason(R): The first few steps are always difficult.

Section – B

Questions 15 and 16 are Case Study based questions and are compulsory. Attempt any 4 sub parts from each question. Each question carries 1 mark.

Question 15.

Figure shows a stress-strain curve for a metal wire which is gradually loaded. The initial part OA of the graph is straight line indicating that stress is proportional to strain. Up to point A, Hooke’s law is obeyed. Portion OB of the graph is called elastic region and the point B is called elastic limit.

1.     The force that is responsible to bring back the shape and size of a body to its original once the deformation force is relieved is called…….

1. Relieving force

2. Restoring force

3. Reformation force

4. Anti-deformation force

 

2. The slope of stress (plotted on Y axis) and strain (plotted on X axis) gives the………… of the material under observation.

1. density

2. conductivity

3. modulus of elasticity

4. All of the above

 

3.     What is the stress-strain curve?
a) It is the percentage of stress and stain
b) It is the relationship between stress and strain
c) It is the difference between stress and strain
d) None of the mentioned

4. What is the point D shown in the stress-strain curve?

a) Lower yield point
b) Elastic limit
c) Proportionality limit
d) Breaking point

5.  Elastic limit is the point………………..
a) up to which stress is proportional to strain
b) At which elongation takes place without application of additional load
c) Up to which if the load is removed, original volume and shapes are regained
d) None of the mentioned

Question 16. A particle executing simple harmonic motion possesses both the potential energy and kinetic energy. The potential energy is due to the displacement of the particle from mean position and the kinetic energy is due to the motion of the particle. The motion of bob of a simple pendulum is considered as Simple harmonic motion.The periodic oscillations periodic whose amplitude decrease gradually with time are known as Damped oscillations.

VARIATION OF KINETIC ENERGY AND POTENTIAL ENERGY

1. The Kinetic energy of a particle executing S.H.M. when it is at mean position is
   (a) Infinite
   (b) Varies
   (c) Maximum
   (d) Zero

2. In SHM, graph of which of the following is a straight line?
   (a) Total energy against displacement
   (b) Potential energy against displacement
   (c) Acceleration against time
   (d) Velocity against displacement

3. In damped oscillations, the angular frequency of the oscillator
   (a) keeps on decreasing
   (b) keeps on increasing
   (c) remains the same
   (d) fluctuates

 

4. In damped oscillations the directions of the restoring force and the resistive force
   (a) are the same
   (b) are opposite
   (c) may be same or opposite
   (d) have no relation with each other

 

5. Time period of simple pendulum of length l and a place where acceleration due to gravity is g is T. what is the period of a simple pendulum of the same length at a place where the acceleration due to gravity is 1.029g is,
   (a) T
   (b) 1.02 T
   (c) 0.99 T
   (d) 1.01 T

Section – C

All questions are compulsory. In case of internal choices, attempt anyone.

17. A physical quantity X is given by X = A2B3/C√D , If the percentage errors of measurement in A,B,C and D are 4%,2%,3% and 1% respectively, then calculate the % error in X.

18. A particle moves along a straight line such that its displacement at any time t is given by s = t3 - 6t2 + 8t + 4) m. What is the velocity of the particle, when its acceleration is zero?

OR

      An object is projected upward with a velocity of 200 ms-1 from the ground. After what time will it strike the ground? Use, g=10 ms-2

19. A body of mass 8 kg placed on a rough horizontal table is connected by a light string passing over a pulley to a hanging body of mass 2 kg. The coefficient of friction between the table and the 8 kg body is 0.1. Find the acceleration of the masses (g = 10 ms-2).

OR

       Define angle of friction and angle of repose. Prove that angle of friction is equal to angle        of Repose.

20.A bomb of mass 10 kg, initially at rest, explodes into two pieces of masses 4 kg and 6 kg. If the speed of the 4 kg piece is 12 ms-1, find the kinetic energy of the 6 kg piece.

21.Where does the centre of mass of a cone lie? Is it necessary that centre of mass always lies inside the body?

22.What are Geostationary satellites? State the necessary conditions (any two) for a satellite to be Geostationary.

23. An artificial satellite revolves around the earth  at a height of 1000km.The radius of earth is 6.38 X 103 km. Mass of earth is 6 X 1024 kg and G=6.67 X10-11 Nm2kg-2.Find its orbital velocity and period of revolution.

24.  Deduce relationship between coefficient of surface expansion and coefficient of linear   expansion.

OR

If the volume of a block of metal changes by 0.12% when it is heated through 200C, what is the coefficient of linear expansion of metal?

25.State the law of equipartition of energy. How much kinetic energy is associated with each molecule of a (i) monoatomic gas (ii) diatomic gas, at T kelvin temperature.

Section-D

All questions are compulsory. In case of internal choices, attempt any one.

26. If the displacement of a body is zero, is the distance covered by it necessarily zero? Comment with suitable illustration.

27. With the help of suitable diagram, obtain an expression for the maximum speed with which a vehicle can safely negotiate a curved road banked at an angle α. The coefficient of friction between the wheels and road is µ.

OR

       What is limiting friction? State the laws of Limiting friction.

28. Prove that in an elastic one-dimensional collision, the relative velocity of approach before collision is equal to the relative velocity of separation after the collision.

OR

       State and prove work energy theorem.

29. What is torque? Show that it is equal to the product of force and the perpendicular distance of its line of action from the axis of rotation.

30. State first law of thermodynamics. On its basis establish the relation between two molar specific heats for a gas.Why is Cp> Cv ?

Section-E

All questions are compulsory. In case of internal choices, attempt any one.

31. (i) A projectile is fired horizontally with velocity u. Show that its trajectory is parabola. 

(ii) A ball is projected horizontally from the top of a building 19.6 m high. If the line joining the point of projection to the point where it hits the ground makes an angle of 45o to the horizontal, what is the initial velocity of the ball? (g = 9.8 m/s2)

OR

(a) An object of mass m is fired from the ground with a velocity u making an angle θ with the horizontal. Derive expressions for (i) Maximum height (ii) horizontal range.

(b) A ball is projected at an angle of 45o to the horizontal. If the horizontal range is 10 m, find the maximum height attained by the ball. (g = 10 m/s2).

32. (i) Show that the sum of pressure head, velocity head and gravitational head remains constant in the streamline flow of an ideal fluid.

      (ii) In streamline flow, water entering a pipe having diameter of 2 cm and the speed of water is 1.0ms-1. Eventually, the pipe tapers to a diameter of 1 cm. calculate the speed of water where diameter of pipe is 1 cm.

OR

1. Derive an expression for the rise of the liquid in a capillary tube.

(ii) What will happen if length of the capillary tube is smaller than the height to which the    liquid rise? Explain briefly.

33. (A) Write Newton’s formula for speed of sound in air. What correction was made by Laplace in this formula?

(B) For a travelling harmonic wave, y=2Cos(10t-0.008x+0.35) where x & y are in cm and t in second. What is the phase difference between oscillatory motions at two points separated by a distance of:

                           (i) 0.5 m ii34

OR

(A) How is the speed of sound in air is affected by

        (i) Pressure (ii) Humidity (iii) Temperature? Give reason.

(B) At what temperature will the speed of sound be double of its value at 273 K?

ANSWER KEY

SET-IV

Q. NO.	Answer/Hint	Weight age
1	[M-1T5]	1
2	Weight of the block (W) = frictional force = μR = 0.2 x 10 = 2N.	1
3	Limiting friction	1
4	No OR Increases	1 1
5	0	1
6	1.26x1012 dyne	1
7	1:2 OR Correct graph	1 1
8	81 times, because E α T4 OR Correct reason	½ + ½ 1
9	The ratio of the average kinetic energy per molecule of the two gases is 1:1 as it depends only on the temperature and is independent of the nature of the gas.	½ +  ½
10	Decreases, because as child stands up, his C.G raised, hence effective length of pendulum decreases.	½ +  ½
11	b	1
12	a	1
13	a	1
14	c	1
15	1.b	1
	2.c	1
	3.b	1
	4.d	1
	5.c	1
16	1.c	1
	2.b	1
	3.c	1
	4.c	1
	5.c	1
17	We have   X=A2B3/CD Then,  ∆XX*100=2∆AA*100+3∆BB*100+∆CC*100+1/2(∆DD)*100 ∆XX*100= 2*4+3*2+1*3+(1/2) *1 ∆XX*100= 8+6+3+0.5 ∆XX*100  =17.5%	1 1212
18	Acceleration is zero at t=2 second Velocity=-4 ms-1 OR Time of ascent=20 second Total time=40 second	1 1 1 1
19	20 – T = 2a T – 0.1 x 80 = 8a Or T – 8 = 8a Solving these, we get a = 1.2 ms-2 OR Statement Proof	1 ½ ½ 1 1
20	Let the speed of the 6 kg piece be v. Then, applying the law of conservation of momentum, 6 v = 4 x 12 or v = 8 m/s K.E. of 6 kg piece = x 6 x (8)2     = 192 J.	½ + ½ 1
21	Correct answer No	1 1
22	Correct definition Two conditions	1 ½ + ½
23	V0 = 7364 ms-1 T=6297 s	1 1
24	Correct relation  Correct final result  OR ϒ=6.0×10-5 per degree Celsius. α=  ϒ/3=2.0×10-5 per degree Celsius.	1 1 1 1
25	Correct Statement Correct answer	1 ½ + ½
26	Correct answer Correct explanation	1 2
27	Correct diagram Correct derivation OR Correct definition Correct statement of four laws	1 2 1 ½ ×4=2
28	Correct diagram Correct Proof OR Correct statement Correct proof	1 2 1 2
29	Correct definition Correct diagram Correct proof	½ 1 112
30	Correct statement Correct derivation Correct answer	1 112 ½
31	Figure Proof Let A be the point of projection and let B be the point where the ball hits the ground. Since ∠ABC = 45o, it is clear that AC = BC                                                  Therefore, Range R = 19.6 m. Time taken to reach the ground                               OR Diagram Derivation for Maximum height Derivation for Horizontal range      . Using  , we get Now, maximum height	12 121 1 1 1 12 121 1 1 1
32	(i)Correct Diagram Correct Proof  (ii) a1v1=a2v2 Solving v2=4.0ms-1                 OR diagram correct derivation  H=2Scosθrρg H=2SRρg HR=Constant HR=H’R’ As H’<H so R’>R Hence in capillary tube of insufficient height the liquid rises to the top and spreads out to a new radius of curvature R’=HRH' the liquid will neither overflow from the upper end like a fountain nor will it tickle along the vertical sides of the tube.	½ 2½ ½ 1½ OR 1 2 2
33	(A)Newton’s formula Laplace correction (B) y=2Cos10t-0.008x+0.35……….(i) We know, y=ACos2πtT-2πx+ϕ……….(ii) From (i) & (ii), 2π=0.008, λ=2π0,008cm=2π0.80m. Phase difference, ϕ=2π*path difference=2π*x. Whenx=0.5m,   ϕ=2π2π*0.80*0.5=0.40rad. Whenx=3λ4,   ϕ=2π*3λ4=3π2rad. OR Correct answer with reason for each part. 1092 K	12 121 12 12 1 1 OR 3×1=3 2