Physics@Viresh_iitk //test -3 for IIT JEE-2012

8/3/2019 Physics@Viresh_iitk //test -3 for IIT JEE-2012

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Section -1 ( straight objective type )

1- A particle is performing SHM. Its potential energy at the mean position is not zero. Then which ofthe following statements is not correct ?

(a) the maximum kinetic energy equals total mechanical energy.(b) the maximum kinetic energy is not equal to maximum potential energy.(c) the total mechanical energy equals maximum potential energy.(d) the sum of potential energy at the mean position and the maximum kinetic energy equalsmaximum potential energy.

2-A particle of mass M is moving on the x-axis, under a force which corresponds to the potentialenergy U = U0 {1 - cos ( bx)} . The particle is found to perform SHM with small amplitude about theorigin. The square of the time period of the particle is proportional to

(a) M / b (b) M / ( U0 b) (c) M / ( U0 b2) (d) MU0 / b

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3- A particle is performing SHM on the x-axis. At the positions x = 2 and x = 6 the directions of theaccelerations are in opposite directions and their magnitudes are in ratio 3 :5. The kinetic energy ofthe particle will be maximum at the position

(a) x = 1.5 (b) x = 2.5 (c) x = 4 (d) x = 3.5

4- The sound velocity at certain temperature in the oxygen is v0 . Now the absolute temperature ofthe gas is doubled and all oxygen molecules are dissociated in to the atoms. Now the sound velocityin the newly formed gas is

(a) v0 (100/21)1/2 (b) v0 (14/25)

1/2 (c) 2v0 (d) v0

5- Two sound sources are sounded together. In the resultant sound , the intensity is varying with time

t as I0 cos2 ( 8 t ) where t is time in seconds. The beats

heard in the sound per second is

(a) 16 (b) 8 (c) 4 (d) none

6- There are two organ pipes A and B. The pipe A is closed at one end and its length is 90 cm. Thepipe B is open at the both ends. Some natural frequencies of both pipes are common. The length ofthe pipe B is not more than 150 cm. What could be the maximum length of B ?

(a) 72 cm (b) 125 cm (c) 60 cm (d) 120 cm

7- A wave is propagating in the negative x- direction with speed 20 m s-1. At time t =0.1 s, the wave

function y at the position x ( meter) is y = a0 sin ( x /2). The value of the wave function y atposition x =0, at time t =0.15 s will be

(a) zero (b) a0 (c) a0 /2 (d) none of these

8- In the arrangement shown, each block A, B and C have equal

mass M and spring constant of the both spring is same. The

upper end of the upper spring is fixed and the all the blocks

are in equilibrium. Suddenly the thread connecting B and C is

cut . Just after this accelerations of the blocks A and B are

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(a) zero & g downward respectively (b) g downward for both

(c) zero & g upward respectively (d) g downward & g upward respectively

9- A uniform ring is allowed to move on an inclined plane, from rest. The ring rolls without slip for 5

seconds and after that the inclined surface was smooth. The ring continued its motion on the

smooth portion for next 5 seconds more. At the end of these 10 seconds of motion. total kinetic

energy of the ring was 60 joules. How much was translational kinetic energy at the end of these 10seconds?

(a) 48 joules (b) 30 joules (c) 42 joules (d) 54 joules

SECTION-2 ( Assertion & Reason type )

In this section four questions are given and each question is followed by two statements.In the answer sheet, mark(a) ifboth the statements are true and statement 2 is correct explanation of the statement1(b) ifboth the statements are true but statement 2 is not correct explanation of thestatement 1

(c) if the statement 1 is true but the statement 2 false(d) if the statement 1 is false but the statement 2 is true.

10-Statement 1 :The velocity of sound in moist air is greater than in dry air.becauseStatement 2 : The moist air has lesser density than that of dry air.

11-Statement 1 : In the organ pipes, the stationary waves, do not change pressure at the free endsbecauseStatement 2 : The pressure change is proportional to the displacement produced by the wave.

12- Statement 1 : All medium particles , lying between two consecutive nodes, oscillates with samephase.because

Statement 2 : The amplitude of the medium particle oscillating due to stationary wave, vary withposition.

13- Statement 1: In SHM, the potential energy changes periodically with same frequency as thedisplacement .because

Statement 2 : In SHM, the change in potential energy , is proportional to the square of thedisplacement from the mean position.

SECTION-3 ( Linked Comprehension Type )

This section contains two paragraphs P14-16 and P17-19 .Each paragraph is followed by 3 questionswith their multiple options for their answers. Choose the only one options which is most correct.

P14-16 : Paragraph for the Q. No 14 to 16A particle is moving on the x-axis. Its kinetic energy at the position x is16- 4 ( x - 5 )2 joules, where x is in meters. The mass of the particle is 0.5 kg.

14-During the motion, the minimum x- coordinate of the particle will be

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(a) 4 m (b) 3 m (c) 5 m (d) 0

15- The nature of the motion of the particle is

(a) oscillatory but not SHM (b) uniformly accelerated motion(c) oscillatory & SHM (d) a motion where acceleration is proportional to x

16-If the particle is seen at rest at time t =0,then how soon it will again be at rest ?

(a) /4 second (b) /2 second (c) second (d) none of these

P17-19 : Paragraph for the Q. No 17 to 19A uniform rod of mass M and length L, is pivoted at its top end.At the lowest end, a horizontal spring of spring constant k isconnected to the rod as shown in the fig. The other end of the springis fixed.

17- The rod is given very small angular displacement

0 ( radian) moving it slowly. The work doneagainst gravity and against the force of spring will be in ratio(a) M g/ ( k L ) (b) 2M g/ ( k L ) (c) 1 : 1 (d) 0.5 M g / ( k L )

18- Let M g = k L . If the rod is released from the very small angular displacement 0 ( radian) , the

magnitude of the angular acceleration of the rod immediately after its release will be 0 multiplied by

(a) 3g / ( 2 L ) (b) 7g /( 2 L ) (c) 9g / ( 2 L) (d) g/ L

19- In the previous problem , assuming M g = k L, after the rod is released , how much time is takento become vertical?

(a) [ M / k]1/2 / 3 (b) [ 2M / k]1/2 /3(c) [ 0.5M / k]1/2 /3 (d) [ 2M / k]1/2 /3

SECTION-4 ( Matrix- Match Type )

20-Let there be a sound source S placed at x =0 and let there be a detector D which records thesound produced by S. The D is placed on the positive x axis at x = L and there is a wall placed at x= -L . In the following column I the state of motion ofS or D or the wall is mentioned and theireffects on the frequency , wavelength and beats recorded by D are given in the column II . Matchthe items in the column I with all the correct descriptions given in the column II and indicate youranswer by darkening appropriate bubbles in the 4 x 4 matrix given . Column I(a) only S moves in positive x - direction (p) no beat is recorded by D(b) only S moves in the negative x -direction (q) some beats are recorded by D(c) only D moves in the negative x -direction (r) sound recorded by D after the

reflection from wall has higherfrequency than original

(d) only wall moves in the positive x -direction (s) sound recorded by D after thereflection from wall has lowerfrequency than original

21-A string fixed at the both ends, has one end at x =0 and other at x =L. Due to a transversestationary wave, the string is oscillating. Consider two points P and Q of the string such that P is at x =L /3 and Q is at x = 2L /3.In the following column I the mode of the oscillation of the string isgiven and in the column II, some properties related to the state of motion of P and Q are mentioned.Match the items in the column I with the correct descriptions given in the column II and indicateyour answer by darkening appropriate bubbles in the 4 x 4 matrix given

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Column I Column II(a) Fundamental mode (p) P and Q are oscillates in same phase(b) 1st over tone (q) P and Q are oscillates in opposite phase(c) 3rd harmonic (r) P and Q acts as node(d) 3rd overtone (s) P and Q are oscillates with same non zero amplitude

22-In the column I some functions of time t , describing the variation of the position coordinates x, yor the position vector r of a particle with time t , are given .Some physical quantities related to theparticle and their description are mentioned in the in the column II. Match the items in the column Iwith the correct descriptions given in the column II and indicate your answer by darkeningappropriate bubbles in the 4 x4 matrix given .

Column I Column II

(A) r = ( 0.6 a i + 0.8 aj ) cos ( t) (p) oscillatory & SHM

(B) x = 2a cos 2 t ; y =0 (q) periodic but not oscillatory

(C) x = a cos( t) + a sin( t - /6) ; y =0 (r) path is straight line

(D) x = 0.8 a sin( t) ; y =0.6 a cos( t) (s) acceleration is always directedtowards origin(0,0)

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Physics@Viresh_iitk //test -3 for IIT JEE-2012

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