Simple Harmonic Motion PYQs Set 3 (PDF)

Set 3 of 11 · Questions 61-90 of 328

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 3 (Q61-90)
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61. $A particle executes S.H.M., the graph of velocity as a function of displacement is:$ (1) $a circle$ (2) $a parabola$ (3) $an ellipse$ (4) $a helix$ 62. $T_{0} is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \frac{1}{16} times of its initial value, the modified time period is:$ (1) $T_{0}$ (2) $8 π T_{0}$ (3) $4 T_{0}$ (4) $\frac{1}{4} T_{0}$ 63. $Choose the correct length (L) versus square of time period (T^{2}) graph for a simple pendulum executing simple harmonic motion.$ (1) (2) (3) (4) 64. $The equation of motion of a particle executing simple harmonic motion is 4 \frac{d ^{2} y}{dt ^{2}} + π^{2} y = 0 where y is in metres and t is in seconds. The time period of oscillation, the particle is$ (1) $1 s$ (2) $2 s$ (3) $3 s$ (4) $4 s$ 65. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Knowing initial position x0 and initial momentum p0 is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency ω. Reason (R): The amplitude and phase can be expressed in terms of x0 and p0. choose the correct answer from the options given below:$ (1) $(A) is false but (R) is true$ (2) $(A) is true but (R) is false$ (3) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ (4) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ 66. $A rectangular block of mass ' M' and cross-sectional area ' A' floats on a liquid of density ' ρ'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ' n' then$ (1) $n \propto A$ (2) $n \propto A^{2}$ (3) $n \propto A$ (4) $n \propto A^{3}$ 67. $A simple pendulum of length L carries a bob of mass m . When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is$ (1) $10 mg$ (2) $5 mg$ (3) $4 mg$ (4) $1 mg$ 68. $The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176rad/s. The frequency of this simple harmonic oscillator is____Hz. [ take π = \frac{22}{7}]$ (1) $14$ (2) $28$ (3) $176$ (4) $88$ 69. $The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N % . The value of N is:$ (1) $4$ (2) $8$ (3) $6$ (4) $5$ 70. $The bob of a simple pendulum performs S.H.M. with period T in air and with period T_{1} in water. Relation between T and T_{1} is (neglect friction due to water, density of the material of the bob = \frac{9}{8} \times 10^{3} kg / m^{3}, density of water 1 g / cc)$ (1) $T_{1} = 3 T$ (2) $T_{1} = 2 T$ (3) $T_{1} = T$ (4) $T_{1} = T 2$ 71. $The displacement of a particle in simple harmonic motion (SHM) is given by y = 3 π sin (\frac{100}{π} t + \frac{π}{4}) . What will be the displacement of the particle from the mean position, when its kinetic energy is eight times that of its potential energy?$ (1) $\frac{π}{3} .$ (2) $\frac{3 π}{2}$ (3) $π$ (4) $3 π$ 72. $A sliver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1 0^{12} /sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of siver =108 and Avagadro number = 6.02 \times 1 0^{23} gm m o l e^{-1})$ (1) $2.2 N/m$ (2) $5.5 N/m$ (3) $6.4 N/m$ (4) $7.1 N/m$ 73. $A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy when its displacement from mean position equals$ (1) $0$ (2) $\pm \frac{A}{2}$ (3) $\pm A$ (4) $\pm \frac{A}{2}$ 74. $The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given: R=Radius of earth and acceleration due to gravity at the surface of earth g = π^{2} m/ s^{- 2})$ (1) $\frac{2}{9} m$ (2) $\frac{4}{9} m$ (3) $\frac{8}{9} m$ (4) $\frac{1}{9} m$ 75. $The angular velocity and the amplitude of a simple pendulum is ω and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is$ (1) $\frac{( a ^{2} - X ^{2} ω ^{2} )}{X ^{2} ω ^{2}}$ (2) $\frac{x ^{2} ω ^{2}}{( a ^{2} - x ^{2} ω ^{2} )}$ (3) $\frac{( a ^{2} - x ^{2} )}{x ^{2}}$ (4) $\frac{x ^{2}}{( a ^{2} - x ^{2} )}$ 76. $The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are A_{1} and A_{2} respectively. If the initial amplitude of the oscillator is A_{0}, then$ (1) $A_{1} = A_{0} A_{2}$ (2) $A_{2} = A_{0} A_{1}$ (3) $A_{0} = A_{1} A_{2}$ (4) $A_{1} = \frac{A _{0} + A _{2}}{2}$ 77. $A particle initially at the mean position is executing simple harmonic motion with an angular frequency \frac{π}{4} rad s^{- 1} . The ratio of the distances travelled by the particle in the first second and second is$ (1) $2 : 1$ (2) $1 : 1$ (3) $(1 + 3) : 1$ (4) $(1 + 2) : 1$ 78. $In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite in direction. (C) The velocity is maximum at mean position. (D) The acceleration is minimum at extreme points. Choose the correct answer from the options given below:$ (1) $(C) and (D) only$ (2) $(A), (C) and (D) only$ (3) $(A), (B) and (C) only$ (4) $(A), (B) and (D) only$ 79. $A spring has a certain mass suspended from it and its period for vertical oscillations is ' T_{1}'. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now " T_{2} . The ratio T_{1} / T_{2} is$ (1) $2$ (2) $2$ (3) $\frac{1}{2}$ (4) $\frac{1}{2}$ 80. $Out of the following functions representing motion of a particle which represents SHM (1) y = sin ω t - cos ω t (2) y = si n^{3} ωt (3) y = 5 cos (\frac{3 π}{4} - 3 ωt) (4) y = 1 + ωt + ω^{2} t^{2}$ (1) $Only (1)$ (2) $Only (4) does not represent SHM$ (3) $Only (1) and (3)$ (4) $Only (1) and (2)$ 81. $Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g, Decay constant = \frac{20 g}{s} then how much time is required for the amplitude of the system to drop to half of its initial value (l n 2 = 0.693)$ (1) $34.65 s$ (2) $17.32 s$ (3) $0.034 s$ (4) $15.01 s$ 82. $A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (B_{Q} : B_{P}) is:$ (1) $3 :4$ (2) $4: 3$ (3) $3 :2$ (4) $2: 3$ 83. $When an oscillator completes 100 oscillations its amplitude reduced to \frac{1}{3} of initial value. What will be its amplitude, when it completes 200 oscillations:$ (1) $\frac{1}{8}$ (2) $\frac{2}{3}$ (3) $\frac{1}{6}$ (4) $\frac{1}{9}$ 84. $Which one of the following equations of motion represents simple harmonic motion? where k, k_{0}, k_{1} and a are all positive.$ (1) $Acceleration = - k (x + a)$ (2) $Acceleration = kx +a$ (3) $Acceleration = kx$ (4) $Acceleration = - k_{g} x + k_{1} x^{2}$ 85. $A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then, its time period (in seconds) is [NEET 2017]$ (1) $\frac{5}{π}$ (2) $\frac{5}{2 π}$ (3) $\frac{4 π}{5}$ (4) $\frac{2 π}{3}$ 86. $A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T_{1} and, (ii) back and forth in a direction perpendicular to its plane, with a period T_{2} . The ratio \frac{T _{1}}{T _{2}} will be$ (1) $\frac{2}{3}$ (2) $\frac{2}{3}$ (3) $\frac{2}{3}$ (4) $\frac{3}{2}$ 87. $In a simple harmonic motion, when the displacement is one‐half the amplitude, what fraction of the total energy is kinetic?$ (1) $1/2$ (2) $3/4$ (3) $zero$ (4) $1/4.$ 88. $A force of 6.4 N stretches a vertical spring by 0.1 m . If it were to oscillate with a period of \frac{π}{4} then the mass that is to be suspended from the spring is$ (1) $\frac{π}{4} kg$ (2) $1 kg$ (3) $\frac{1}{π} kg$ (4) $10 kg$ 89. $The displacement equation of a particle is x = 3 sin 2t + 4 cos 2t, where x is in meter and t in second. The amplitude and maximum velocity will be respectively:$ (1) $5m, 10 m/s$ (2) $3m, 2 m/s$ (3) $4m, 2 m/s$ (4) $3m, 4 m/s$ 90. $A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of$ (1) $0 rad$ (2) $\frac{π}{4} rad$ (3) $\frac{π}{2} rad$ (4) $πrad$