Simple Harmonic Motion PYQs Set 8 (PDF)

Set 8 of 11 · Questions 211-240 of 328

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 8 (Q211-240)
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211. $A particle undergoing simple harmonic motion has time dependent displacement given by x (t) = A sin \frac{πt}{90} . The ratio of kinetic to potential energy of this particle at t = 210 s will be$ (1) $1/9$ (2) $1$ (3) $1/3$ (4) $1/2$ 212. $Two simple pendulums A and B are made to oscillate simultaneously and it is found that A completes 10 oscillations in 20 s and B completes 8 oscillations in 10 s . The ratio of the lengths of A and B is$ (1) $5/4$ (2) $8/5$ (3) $25/64$ (4) $64/25$ 213. $A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm / s . The frequency of its oscillation is$ (1) $4 Hz$ (2) $3 Hz$ (3) $2 Hz$ (4) $1 Hz.$ 214. $A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude 12 cm . After 2 minutes the amplitude decreasesto 6 cm . Determine the value of the dampingconstant for this motion. (take In 2 = 0.693)$ (1) $0.69 \times 10^{2} kg s^{- 1}$ (2) $3.3 \times 10^{2} kg s^{- 1}$ (3) $1.16 \times 10^{- 2} kg s^{- 1}$ (4) $5.7 \times 10^{- 3} kg s^{- 1}$ 215. $If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the placewhere pendulum is executing S.H.M. is:$ (1) $2 π^{2} ms^{- 2}$ (2) $16 m / s^{2}$ (3) $9.8 ms^{- 2}$ (4) $π^{2} ms^{- 2}$ 216. $A 20 g particle is subjected to two simple harmonic motions x_{1} = 2 sin 10 t x_{2} = 4 sin (10 t + \frac{π}{3}) . where x_{1} and x_{2} are in metre and t is in sec. Choose the incorrect option.$ (1) $The displacement of the particle at t = 0 will be 23 m$ (2) $Maximum speed of the particle will be 207 m / s$ (3) $Magnitude of maximum acceleration of the particle will be 2007 m / s^{2}$ (4) $Energy of the resultant motion will be 26 J$ 217. $When an external force with angular frequency ω_{d} acts on a system of natural angular frequency ω, the system oscillates with angular frequency ω_{d} . The condition for the amplitude of oscillations to be maximum is$ (1) $ω_{d} = 2 ω$ (2) $ω_{d} = ω$ (3) $ω_{d} = \frac{ω}{2}$ (4) $ω_{d} = 3 ω$ 218. $A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is \frac{3 E}{4} then its displacement 'y' is given by:$ (1) $y = a$ (2) $y = \frac{a}{2}$ (3) $y = \frac{a 3}{2}$ (4) $y = \frac{a}{2}$ 219. $A particle executes SHM of amplitude A. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:$ (1) $\frac{1}{2} A$ (2) $2A$ (3) $2 A$ (4) $\frac{1}{2} A$ 220. $Two SHM’s with same amplitude and time period, when acting together in perpendicular directions with a phase difference of π /2, give rise to$ (1) $straight motion$ (2) $elliptical motion$ (3) $circular motion$ (4) $none of these.$ 221. $A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T . The sphere is now immersed in a non-viscous liquid with a density (1/10) th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be$ (1) $(\frac{9}{10}) T$ (2) $(\frac{10}{9}) T$ (3) $(\frac{9}{10}) T$ (4) $Unchanged$ 222. $The amplitude of a simple pendulum is 10 cm . When the pendulum is at a displacement of 4 cm from the mean position, the ratio of kinetic and potential energies at that point is$ (1) $5.25$ (2) $2.5$ (3) $4.5$ (4) $7.5$ 223. $A loaded vertical spring executes S.H.M. with a time period of 4 sec. The difference between the kinetic energy and potential energy of this system varies with a period of$ (1) $2 sec$ (2) $1 sec$ (3) $8 sec$ (4) $4sec.$ 224. $Time period of a simple pendulum of length ' L' is T_{1} . Time period of a uniform rod of same length ' L' suspended from one end and oscillating in a vertical plane is T_{2} . Amplitude of oscillation is small in both the cases. Then \frac{T _{1}}{T _{2}} is$ (1) $\frac{2}{3}$ (2) $\frac{3}{2}$ (3) $\frac{4}{3}$ (4) $1$ 225. $The time period of a simple pendulum on the surface of the earth is T. The height above the surface of the earth at which the time period of the pendulum becomes 2 T is (Radius of the earth = 6400 km)$ (1) $3200 km$ (2) $6400 km$ (3) $1600 km$ (4) $800 km$ 226. $Which graph represents the difference between total energy and potential energy of a particle executing SHM vs its distance from mean position?$ (1) (2) (3) (4) 227. $Which of the following quantity does not change due to damping of oscillations?$ (1) $Angular frequency$ (2) $Time period$ (3) $Initial phase$ (4) $Amplitude$ 228. $If the length of a simple pendulum is increased by 2%, then the time period$ (1) $increases by 1%$ (2) $decreases by 1%$ (3) $increases by 2%$ (4) $decreases by 2%.$ 229. $A particle performs simple harmonic motion with a time period of 16 s . At a time t = 2 s, the particle passes through the origin and at t = 4 s its velocity is 4 m / s . The amplitude of the motion is$ (1) $32 π 2.$ (2) $\frac{32 2}{π}$ (3) $32 π$ (4) $32$ 230. $A block of mass 100 g moving at a speed of 2 m / s compresses a spring through a distance 2 cm before its speed is halved. Find the spring constant of the spring.$ (1) $12500 N / m$ (2) $750 N / m$ (3) $1000 N / m$ (4) $1500 N / m$ 231. $A tray of mass 12 kg is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of 1, 5 s . The spring constant of each spring is$ (1) $105 N m^{- 1}$ (2) $\infty$ (3) $50 N m^{- 1}$ (4) $0$ 232. $Two masses m and \frac{m}{2} are connected at the two ends of a massless rigid rod of length λ. The rod is suspended by a thin wire of torsional constant k at the center of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is τ = kθ. for angular displacement θ. If the rod is rotated by θ_{0.} and released, the tension in it when it passes through its mean position will be:$ (1) $\frac{3 k θ _{0}^{2}}{l}$ (2) $\frac{k θ _{0}^{2}}{2 l}$ (3) $\frac{2 k θ _{0}^{2}}{l}$ (4) $\frac{k θ _{0}^{2}}{l}$ 233. $A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density ρ . If the mass of hydrometer is m and the radius of the hydrometer tube is r, then the time period of oscillation is$ (1) $T = 2 π \frac{m}{π r ^{2} ρg}$ (2) $T = 2 π \frac{π r ^{2} ρg}{m}$ (3) $T = \frac{1}{2 π} \frac{m}{π r ^{2} ρg}$ (4) $T = \frac{1}{2 π} \frac{π r ^{2} ρg}{m}$ 234. $Two springs, of force constants k_{1} and k_{2}, are connected to a mass m as shown. The frequency of oscillation of mass is ƒ. If both k_{1} and k_{2} are made four times their original values, the frequency of oscillation becomes:$ (1) $ƒ/2$ (2) $ƒ/4$ (3) $4f$ (4) $2ƒ$ 235. $The displacement time graph of a particle executing SHM is given in figure (sketch is schematic and not to scale) Which of the following statements is/are true for this motion? (A) The force is zero at t = \frac{3 T}{4} (B) The acceleration is maximum at t=T (C) The speed is maximum at t = \frac{T}{4} (D) The P.E. is equal to K.E. of the oscillation at t = \frac{T}{2}$ (1) $(B), (C) and (D)$ (2) $(A) and (D)$ (3) $(A), (B) and (C)$ (4) $(A), (B) and (D)$ 236. $For particle P revolving round the centre O with radius of circular path r and regular velocity a, as shown in below figure, the projection of OP on the x-axis at time t is$ (1) $x (t) = r cos (ωt - \frac{π}{6})$ (2) $x (t) = r cos (ωt + \frac{π}{6})$ (3) $x (t) = r sin (ωt + \frac{π}{6})$ (4) $x (t) = r cos (ωt)$ 237. $A simple pendulum of length l has maximum angular displacement θ . The maximum kinetic energy of the bob of mass m is (g = acceleration due to gravity)$ (1) $mgl (1 + cos θ)$ (2) $mgl (1 + cos^{2} θ)$ (3) $mgl (1 - cos θ)$ (4) $mgl (cos θ - 1)$ 238. $As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is : k = 150 N / m$ (1) $5$ (2) $27$ (3) $20$ (4) $30$ 239. $Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length ‘r. What is the equilibrium separation when each thread makes a small angle ' θ' with the vertical?$ (1) $x = (\frac{q ^{2} l}{2 π ϵ _{0} mg})^{\frac{1}{2}}$ (2) $x = (\frac{q ^{2} l}{2 π ϵ _{0} mg})^{\frac{1}{3}}$ (3) $x = (\frac{q ^{2} l ^{2}}{2 π ϵ _{0} m ^{2} g})^{\frac{1}{3}}$ (4) $x = (\frac{q ^{2} l ^{2}}{2 π ϵ _{0} m ^{2} g ^{2}})^{\frac{1}{3}}$ 240. $A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed 60 cm^{- 1} on the string, when the car is at rest. When the car accelerates on a horizontal road, then speed of the pulse is 66 cm^{- 1} . The acceleration of the car is nearly (g = 10 ms^{- 2})$ (1) $4.3 ms^{- 2}$ (2) $2.9 ms^{- 2}$ (3) $6.8 ms^{- 2}$ (4) $5.5 ms^{- 2}$