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1 SR IIT ALL STREAMS ADV MODEL DPT-6 Date: 18/04/2016 One (or) More Than One Answer Type: PHYSICS 31. A particle is executing SHM between points -X m and X m, as shown in figure-i. The velocity V(t) of the particle is partially graphed and shown in figure-ii. Two points A and B corresponding to time t 1 and time t 2 respectively are marked on the V(t) curve. V +x B -X m O X m Figure-I t 1 t 2 A Figure-II t (A) At time t 1, it is going towards X m. (B) At time t 1, its speed is decreasing. (C) At time t 2, its position lies in between X m and O. (D) The phase difference between points A and B must be expressed as 90 < < The amplitude of a particle executing SHM about O is 10 cm. Then: (A) when the K.E. is 0.64 of its maximum K.E. its displacement is 6 cm from O. (B) when the displacement is 5 cm from O its K.E. is 0.75 times its maximum K.E. (C) Its total energy of SHM at any point is equal to its maximum K.E. (D) Its speed is half the maximum speed when its displacement is half the maximum displacement. 33. Two blocks of masses 3 kg and 6 kg rest on a horizontal smooth surface. The 3 kg block is attached to a spring with a force constant k = 900 Nm -1 which is compressed 2 m from beyond the equilibrium position. The 6 kg mass is at rest at 1m from mean position. 3kg mass strikes the 6 kg mass and the two stick together. (A) velocity of the combined masses immediately after the collision is 10 ms -1 (B) velocity of the combined masses immediately after the collision is 5 ms -1 (C) Amplitude of the resulting oscillation is 2 m (D) Amplitude of the resulting oscillation is 5/2 m. 34. Two blocks A (5kg) and B(2kg) attached to the ends of a spring constant 1120N/m are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of 3m/s and 10m/s along the line of the spring in the same direction are imparted to A and B then 5kg k = 1120 N/m 2kg 1
2 (A) when the extension of the spring is maximum the velocities of A and B are zero. (B) the maximum extension of the spring is 25cm. (C) the first maximum compression occurs 3/56 seconds after start. (D) maximum extension and maximum compression occur alternately. 35. At t = 0 the displacement of the block in a linear oscillator executing SHM along an x-axis as shown is 0.08m. At the same moment t = 0, its velocity is m/s and acceleration is 32 m/s 2. K m X m X=0 +X m (A) (B) (C) (D) Angular freequency of the motion is 20 rad/s. Amplitude of the motion is 11.3 cm. Phase constant of the motion if the equation of motion is expressed as x = A sin(t + ) is 4 5 Phase constant of the motion if the equation of motion is expressed as x = A sin(t + ) is The position of a particle w.r. to origin varies according to the relation x = 3 sin 100t + 8 cos 2 50t. Which of the following is/are correct about this motion. (A) the motion of the particle is not S.H.M. (B) the amplitude of the S.H.M. of the particle is 5 units (C) the amplitude of the resultant S.H. M. is 73 units (D) the maximum displacement of the particle from the origin is 9 units. 37. A 20 gm particle is subjected to two simple harmonic motions x 1 = 2 sin 10 t, x 2 = 4 sin (10 t + 3 ). where x1 & x 2 are in metre & t is in sec. (A) The displacement of the particle at t = 0 will be 2 3 m. (B) Maximum speed of the particle will be 20 7 m/s. (C) Magnitude of maximum acceleration of the particle will be m/s 2. (D) Energy of the resultant motion will be 28 J. 38. S 1 and S 2 are two coherent sources of sound of frequency 110Hz each. They have no initial phase difference. The intensity at a point P due to S 1 is 0 and due to S 2 is 4 0. If the velocity of sound is 330 m/s then 2 (A)the phase difference between the two sond waves at Pis 3 (B) the phase difference between the two sond waves at P is 3 (C) the resultant intensity at P is 3I 0 (D) the resultant intensity at P is 7I 0 2
3 39. In the figure shown an observer O 1 floats (static) on water surface with ears in air while another observer O 2 is moving upwards with constant velocity V 1 = V/5 in water. The source moves down with constant velocity V s = V/5 and emits sound of frequency 'f'. The velocity of sound in air is V and that in water is 4V. For the situation shown in figure : S V s = V 5 O 1 V 1 = V 5 O 2 (A) The wavelength of the sound received by O 1 is 4V 5f (B) The wavelength of the sound received by O 1 is V/f 21f (C) The frequency of the sound received by O 2 is 16 (D) The wavelength of the sound received by O 2 is 40. A car moves towards a hill with speed v c. It blows a horn of frequency f which is heard by an observer following the car with speed v 0. The speed of sound in air is v. (A) the wavelength of sound reaching the hill is v f (B) the wavelength of sound reaching the hill is v v c f 16V 5f (C) The wavelength of sound of horn directly reaching the observer is (D) the beat frequency observed by the observer is 2v c 2 v v v v o 2 c f v v f 41. A wire of density kg/m 3 is stretched between two clamps 1 m apart and is stretched to an extension of metre. Young's modulus of material is N/m 2. Then (A) The lowest frequency of standing wave is 35 Hz (B) The frequency of 1st overtone is 70 Hz (C) The frequency of 1st overtone is 105 Hz (D) The stress in the wire is N/m One end of a string of length L is tied to the ceiling of a lift accelerating upwards with an acceleration 2g. The other end of the string is free. The linear mass density of the string varies linearly from 0 to from bottom to top. (A) The velocity of the wave in the string will be 0. (B) The acceleration of the wave on the string will be 3g/4 every where. (C) The time taken by a pulse to reach from bottom to top will be 8L / 3g. (D) The time taken by a pulse to reach from bottom to top will be 4L / 3g. c 3
4 43. y-x curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A on the curve, as shown, is 53. y A 53 x (A) Transverse velocity of the particle at point A is positive if the wave is travelling along positive x axis. (B) Transverse velocity of the particle at point A is positive if the wave is travelling along negative x axis of the particle at point A (C) Magnitude of transverse velocity of the particle at point A is greater than wave speed. (D) Magnitude of transverse velocity of the particle at point A is lesser than wave speed. 44. If the tension in a stretched string fixed at both ends is increased by 21%, the fundamental frequency is found to change by 15Hz. Then the (A) original frequency is 150Hz (B) velocity of propagation of the transverse wave along the string increases by 5% (C) velocity of propagation of the transverse wave along the string increases by 10% (D) fundamental wave length on the string does not change. 45. For a certain transverse standing wave on a long string, an antinode is formed at x = 0 and next to it, a node is formed at x = 0.10 m. the displacement y(t) of the string particle at x = 0 is shown in figure. 4 y(cm) t(s) -4 (A) Transverse displacement of the particle at x = 0.05m and t = 0.05 s is 2 2 cm. (B) Transverse displacement of the particle at x = 0.04 m and t = s is 2 2 cm. (C) Speed of the travelling waves that interfere to produce this standing wave is 2 m/s. 1 (D) The transverse velocity of the string particle at x = m and t = 0.1 s is 20 cm/s A particle of mass m performs SHM along a straight line with frequency f and amplitude A. (A) The average kinetic energy of the particle is zero. (B) The average potential energy is m 2 f 2 A 2. (C) The frequency of ocillation of kinetic energy is 2f. (D) Velocity function leads acceleration by / A spring has natural length 40 cm and spring constant 500 N/m. A block of mass 1 kg is attached at one end of the spring and other end of the spring is attached to ceiling. The block released from the position, where the spring has length 45 cm. (A) the block will perform SHM of amplitude 5 cm. (B) the block will have maximum velocity 30 5 cm/sec. (C) the block will have maximum acceleration 15 m/s 2 (D) the minimum potential energy of the spring will be zero. 4
5 48. A mass of 0.2kg is attached to the lower end of a massless spring of force-constant 200 N/m, the upper end of which is fixed to a rigid support. Which of the following statements is/are true? (A) In equilibrium, the spring will be stretched by 1cm. (B) If the mass is raised till the spring is unstretched state and then released, it will go down by 2cm before moving upwards. (C) The frequency of oscillation will be nearly 5 Hz. (D) If the system is taken to the moon, the frequency of oscillation will be the same as on the earth. 49. The two blocks shown here rest on a frictionless surface. If they are pulled apart by a small distance and released at t = 0, the time when 1 kg block comes to rest can be 2 (A) sec. (B) sec. (C) sec. (D) sec The potential energy of a particle of mass 0.1kg, moving along x-axis, is given by U = 5x(x-4)J where x is in metres. It can be concluded that (A) the particle is acted upon by a constant force. (B) the speed of the particle is maximum at x = 2 m (C) the particle executes simple harmonic motion (D) the period of oscillation of the particle is /5 s. 51. A disc of mass 3m and a disc of mass m are connected by a massless spring of stiffness k. The heavier disc is placed on the ground with the spring vertical and lighter disc on top. From its equilibrium position, the upper disc is pushed down by a distance and released. Then (A) if > 3mg/k, the lower disc will bounce up (B) if = 2mg/k, maximum normal reaction from ground on lower disc = 6 mg. (C) if = 2mg/k, maximum normal reaction from ground on lower disc = 4 mg. (D) if > 4mg/k, the lower disc will bounce up 52. A particle moves in xy plane according to the law x = a sint and y = a(1-cost),where a and are constants. The particle traces (A) a parabola (B) a straight line equallyinclined to x and y axes (C) a circle (D) a distance proportional to time. 53. At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points P, Q and R on the string. (A) v P is upwards (B) v Q = v R (C) v P > v Q = v R (D) v Q = v R 54. A clamped string is oscillating in nth harmonic, then (A) total energy of oscillations will be proportional to n 2 times that of fundamental frequency (B) total energy of oscillations will be proportional to (n 1) 2 times that of fundamental frequency (C) average kinetic energy of the string over a complete oscillations is half of that of the total energy of the string. (D) none of these 5
6 55. A transverse sinusoidal wave of amplitude a, wavelength & frequency f is travelling on a stretched string. The maximum speed of any point on the string is v, where v is speed of propagation 10 of the wave. If a = 10 3 m and v = 10 ms 1, then & f are given by : (A) = 2 x 10 2 m (B) = 10 2 m (C) f = 10 2 Hz (D) f = 104 Hz 56. Which of the following statements are wrong about the velocity of sound in air: (A) decreases with increases in temperature (B) increases with decrease in temperature (C) decreases as humidity increases (D) independent of density of air. 57. A gas is filled in an organ pipe and it is sounded in fundamental mode. Choose the correct statement(s) : (T = constant) (A) If gas is changed from H 2 to O 2, the resonant frequency will increase (B) If gas is changed from O 2 to N 2, the resonant frequency will increase (C) If gas is changed from N 2 to He, the resonant frequency will decrease (D) If gas is changed from He to CH 4, the resonant frequency will decrease 58. Two whistles A and B each have a frequency of 500Hz. A is stationary and B is moving towards the right (away from A) at a speed of 50 m/s. An observer is between the two whistles moving towards the right with a speed of 25 m/s. The velocity of sound in air is 350 m/s. Assume there is no wind. Then which of the following statements are true: (A) The apparent frequency of whistle B as heard by A is 444Hz approximately (B) The apparent frequency of whistle B as heard by the observer is 469Hz approximately (C) The difference in the apparent frequencies of A and B as heard by the observer is 4.5 Hz. (D) The apparent frequencies of the whistles of each other as heard by A and Bare the same. 59. The second overtone of an open organ pipe A and a closed pipe B have the same frequency at a given temperature. It follows that the ratio of the (A) length of A and B is 4 : 3 (B) fundamental frequencies of A & B is 5 : 6 (C) lengths of B to that of A is 5 : 6 (D) frequencies of first overtone of A & B is 10 : The displacement-time graph of a particle executing SHM is shown. 3 Which of the following statements is/are true? (A) The velocity is maximum at t = T/2 (B) The acceleration is maximum at t = T (C) The force is zero at t = 3T/4 (D) The potential energy equals the oscillation energy at t = T/2. 6
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