Simple Harmonic Motion PYQs Set 4 (PDF)

Set 4 of 11 · Questions 91-120 of 328

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 4 (Q91-120)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
91. $A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 \times 10^{- 6} J / T when a magnetic intensity of 60 \times 10^{3} A / m is applied. Its magnetic susceptibility is:$ (1) $3.3 \times 10^{- 2}$ (2) $4.3 \times 10^{- 2}$ (3) $2.3 \times 10^{- 2}$ (4) $3.3 \times 10^{- 4}$ 92. $An object of mass 0.5kg is executing simple harmonic motion. Its amplitude is 5 cm and time period (T) is 0.2s. What will be the potential energy of the object at an instant t = \frac{T}{4} s starting from mean position. Assume that the initial phase of the oscillation is zero.$ (1) $0.62J$ (2) $6.2\times 1 0^{- 3} J$ (3) $1.2 \times 1 0^{- 3} J$ (4) $3.1\times 1 0^{- 3} J$ 93. $If x, V and a denote the displacement, velocity and acceleration of a particle respectively executing simple harmonic motion of periodic time T, then which one of the following does not change with time?$ (1) $\frac{aT}{x}$ (2) $aT + 2 πV$ (3) $\frac{aT}{V}$ (4) $aT + 4 π^{2} V^{2}$ 94. $A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . The length of the string required for the pendulum to perform 40 oscillations in the same time duration is____cm . [Assume that the mass of the pendulum remains same.]$ (1) $7.5$ (2) $0.75$ (3) $120$ (4) $15$ 95. $The displacement of a particle varies according to the relation x = 4 (cos πt + sin πt). The amplitude of the particle is$ (1) $4$ (2) $2$ (3) $42$ (4) $8$ 96. $For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?$ (1) $x = 0$ (2) $x = \pm A$ (3) $x = \pm \frac{A}{2}$ (4) $x = \frac{A}{2}$ 97. $A simple pendulum of length 1 m is freely suspended from the ceiling of an elevalor. The time period of small oscillations as the elevator moves up with an acceleration of 2 m / s^{2} is (use g = 10 m / s^{2})$ (1) $\frac{π}{5} s$ (2) $\frac{2}{5} πs$ (3) $\frac{π}{2} s$ (4) $\frac{π}{3} s$ 98. $A mass m_{1} connected to a horizontal spring performs S.H.M. with amplitude A . While mass m_{1} is passing through mean position another mass m_{2} is placed on it so that both the masses move together with amplitude A_{1} . The ratio of \frac{A _{1}}{A} is (m_{2} < m_{1})$ (1) $(\frac{m _{1}}{m _{1} + m _{2}})^{\frac{1}{2}}$ (2) $(\frac{m _{1} + m _{2}}{m _{1}})^{\frac{1}{2}}$ (3) $(\frac{m _{2}}{m _{1} + m _{2}})^{\frac{1}{2}}$ (4) $(\frac{m _{1} + m _{2}}{m _{2}})^{\frac{1}{2}}$ 99. $For a particle performing linear S.H.M., its average speed over one oscillation is (a = amplitude of S.H.M., n = frequency of oscillation)$ (1) $2 an$ (2) $4 an$ (3) $6 an$ (4) $8 an$ 100. $The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:$ (1) $k g m s^{-1}$ (2) $k g m s^{-2}$ (3) $k g s^{-1}$ (4) $kgs$ 101. $For a particle executing SHM, determine the ratio of average acceleration of the particle between extreme position and equilibrium position w.r.t. the maximum acceleration.$ (1) $\frac{4}{π}$ (2) $\frac{2}{π}$ (3) $\frac{1}{π}$ (4) $\frac{1}{2 π}$ 102. $A body is executing simple harmonic motion. When the displacements from the mean position is 4 cm and 5 cm, the corresponding velocities of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is$ (1) $2 π sec$ (2) $π /2 sec$ (3) $πsec$ (4) $3 π /2 sec$ 103. $The position of a particle in motion is given by y = C sinꞷt + D cosꞷt w.r.t. origin. Then motion of the particle is:$ (1) $SHM with amplitude C+D$ (2) $SHM with amplitude C^{2} + D^{2}$ (3) $SHM with amplitude \frac{( C + D )}{2}$ (4) $not SHM$ 104. $When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be:$ (1) $Circular$ (2) $Ellipitical$ (3) $Sinusoidal$ (4) $Straight line$ 105. $The time taken for the amplitude of vibrations of a damped oscillator to drop to 25 % of its initial value is t . The time taken for its mechanical energy to drop to 50 % of its initial mechanical energy is$ (1) $t$ (2) $\frac{t}{2}$ (3) $\frac{t}{4}$ (4) $\frac{t}{8}$ 106. $A piston is performing S.H.M. in the vertical direction with a frequency of 0.5 Hz . A block of 10 kg is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is$ (1) $1.5 m$ (2) $1 m$ (3) $0.1 m$ (4) $0.5 m$ 107. $The amplitude of a damped oscillator is known to decrease to 0.9 times its original amplitude in 5 s. Approximately, by how many times its original amplitude will decrease after another 20 s?$ (1) $0.73$ (2) $0.9$ (3) $0.59$ (4) $0.26$ 108. $Using a simple pendulum experiment g is determind by measuring its time period T . Which of the following plots represent the correct relation between the pendulum length L and time period T ?$ (1) (2) (3) (4) 109. $The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is$ (1) $100 s$ (2) $0.01 s$ (3) $10 s$ (4) $0.1 s$ 110. $The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out the time period of oscillation would$ (1) $remain unchanged$ (2) $increase towards a saturation value$ (3) $first increase and then decrease to the original value$ (4) $first decrease and then increase to the original value$ 111. $A light spring is suspended with mass m_{1} at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass m_{2} is added to m_{1} and the system is made to oscillate, the period is found to be \frac{3}{2} T . The ratio of m_{1} : m_{2} is$ (1) $2 : 3$ (2) $3 : 4$ (3) $4 : 5$ (4) $5 : 6$ 112. $Average velocity of a particle executing SHM in one complete vibration is [NEET 2019]$ (1) $Aω$ (2) $Aω 22$ (3) $zero$ (4) $Aω 2$ 113. $In case of a forced vibration, the resonance wave becomes very sharp when the$ (1) $Restoring force is small$ (2) $Applied periodic force is small$ (3) $Quality factor is small$ (4) $Damping force is small$ 114. $The density of a material in SI unit of is 128 kg m^{- 3} In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is:$ (1) $40$ (2) $16$ (3) $640$ (4) $410$ 115. $If the displacement equation of a particle be represented by y = A sin PT + B cos PT, the particle executes.$ (1) $A uniform circular motion$ (2) $A uniform elliptical motion$ (3) $A S.H.M.$ (4) $A rectilinear motion$ 116. $A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sin ω t . If the amplitude of the particle is maximum for co = co1 and the energy of the particle is maximum for ω = ω_{2}, then$ (1) $ω_{1} \neq = ω_{0} and ω_{2} = ω_{0}$ (2) $ω_{1} = ω_{0} and ω_{2} = ω_{0}$ (3) $ω_{1} = ω_{0} and ω_{2} \neq = ω_{0}$ (4) $ω_{1} \neq = ω_{0} and ω_{2} \neq = ω_{0}$ 117. $The displacement of a damped harmonic oscillator is given by x (t) = e^{- 0.1 t} \cdot cos (10 πt + ϕ) . Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:$ (1) $4 s$ (2) $7 s$ (3) $13 s$ (4) $27 s$ 118. $The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 \times 1 0^{-2} cosπt metres. The time at which the maximum speed first occurs is:$ (1) $0.5 s$ (2) $0.75 s$ (3) $0.125 s$ (4) $0.25 s$ 119. $A rectangular block of mass m and area of cross‐section A floats in a liquid of density p . If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then$ (1) $T \propto \frac{1}{m}$ (2) $T \propto p$ (3) $T \propto \frac{1}{A}$ (4) $T \propto \frac{1}{p}$ 120. $Two simple pendulums having lengths l_{1} and l_{2} with negligible string mass undergo angular displacements θ_{1} and θ_{2}, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?$ (1) $θ_{1} l_{2} = θ_{2} l_{1}$ (2) $θ_{1} l_{1} = θ_{2} l_{2}$ (3) $θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$ (4) $θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$