Simple Harmonic Motion PYQs Set 10 (PDF)

Set 10 of 11 · Questions 271-300 of 328

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 10 (Q271-300)
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271. $Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R /2 from the earth'scenter, where ’ R ’ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in thistunnel, it will execute a simple harmonic motion with a time period:$ (1) $2 π \frac{R}{g}$ (2) $\frac{1}{2 π} \frac{g}{R}$ (3) $\frac{2 πR}{g}$ (4) $\frac{g}{2 πR}$ 272. $A particle executes simple harmonic motion between x = -A and x = +A. If time taken by particle to go from x = 0 to \frac{A}{2} is 2s; then time A taken by particle in going from x= \frac{A}{2} to A is:$ (1) $3s$ (2) $2s$ (3) $1.5s$ (4) $4s$ 273. $The x -t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2 s is [NEET 2023]$ (1) $- \frac{π ^{2}}{8} ms^{- 2}$ (2) $\frac{π ^{2}}{16} ms^{- 2}$ (3) $- \frac{π ^{2}}{16} ms^{- 2}$ (4) $\frac{π ^{2}}{8} ms^{- 2}$ 274. $9 kg . solution is poured into a glass U-tube as shown in the figure below. The tube's inner diameter is 2 \frac{π}{5} m and the solution oscillates freely up and down about its position of equilibrium (x = 0) . The period of oscillation in seconds is (1 m^{3}) of solution has a mass μ = 900 kg, g = 10 m / s^{2}, ignore frictional and surface tension effects)$ (1) $0.1$ (2) $10$ (3) $π$ (4) $1$ 275. $A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle (θ) of thread deflection in the extreme position will be:$ (1) $tan^{- 1} (2)$ (2) $2 tan^{- 1} (\frac{1}{2})$ (3) $tan^{- 1} (\frac{1}{2})$ (4) $2 tan^{- 1} (\frac{1}{5})$ 276. $A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N / m . The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be$ (1) $10 (1 - (2 - x)^{2})^{\frac{1}{2}} m / s$ (2) $10 (1 - (2 - x)^{2})^{\frac{3}{2}} m / s$ (3) $10 (1 - (2 - x)^{2}) m / s$ (4) $10 (1 - (2 - x)^{2})^{2} m / s$ 277. $Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?$ (1) $When v is maximum, a is maximum.$ (2) $Value of a is zero, whatever may be the value of v .$ (3) $When v is zero, a is zero.$ (4) $When v is maximum, a is zero.$ 278. $Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is$ (1) $\pm a /2$ (2) $+ a$ (3) $\pm a$ (4) $- 1 .$ 279. $The period of oscillation of a mass A4 suspended from a spring of negligible mass is T . If along with it another mass M is also suspended, the period of oscillation will now be$ (1) $T$ (2) $\frac{T}{2}$ (3) $2 T$ (4) $2 τ$ 280. $A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T . The speed of the pendulum at x = a /2 will be$ (1) $\frac{πa}{T}$ (2) $\frac{3 π ^{2} a}{T}$ (3) $\frac{πa 3}{T}$ (4) $\frac{πa 3}{2 T}$ 281. $A vertical spring mass system has the same time period as simple pendulum undergoing small oscillations. Now, both of them are put in an elevator going downwards with an acceleration 5 m / s^{2} . The ratio of time period of the spring mass system to the time period of the pendulum is (Assume, acceleration due to gravity, = 10 m / s^{2})$ (1) $\frac{3}{2}$ (2) $\frac{2}{3}$ (3) $\frac{1}{2}$ (4) $2$ 282. $A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is:$ (1) $\frac{9}{16}$ (2) $\frac{3}{4}$ (3) $\frac{4}{3}$ (4) $\frac{16}{9}$ 283. $The mass M shown in the figure oscillates in simple harmonic motion with amplitude A . The amplitude of point P is$ (1) $\frac{k _{1} A}{k _{2}}$ (2) $\frac{k _{2} A}{k _{1}}$ (3) $\frac{k _{1} A}{k _{1} + k _{2}}$ (4) $\frac{k _{2} A}{k _{1} + k _{2}}$ 284. $A mass of 5kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?$ (1) $10m/ s^{2}$ (2) $5m/ s^{2}$ (3) $4 m/ s^{2}$ (4) $9.8 m/ s^{2}$ 285. $A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered by the particle in 12.5 s, then \frac{D}{d} is$ (1) $\frac{16}{5}$ (2) $10$ (3) $\frac{15}{4}$ (4) $25$ 286. $A particle starts with S.H.M. from the mean position as shown in the figure. Its amplitude is A and its time period is T . At one time, its speed is half that of the maximum speed. What is this displacement?$ (1) $\frac{2 A}{3}$ (2) $\frac{3 A}{2}$ (3) $\frac{2 A}{3}$ (4) $\frac{3 A}{2} .$ 287. $The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the below figure. [NEET 2019] y -projection of the radius vector of rotating particle P is$ (1) $y (t) = 4 sin (\frac{πt}{2}), where y in m$ (2) $y (t) = 3 cos (\frac{3 πt}{2}), where y in m$ (3) $y (t) = 3 cos (\frac{πt}{2}), where y in m$ (4) $y (t) = - 3 cos 2 πt, where y in m$ 288. $A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:$ (1) $1:2$ (2) $1:1$ (3) $2:3$ (4) $2:5$ 289. $Two identical spring of spring constant ’ 2 K ’ are attached to a block of mass m and to fixed support (seefigure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then time period of oscillations of this system is:$ (1) $π \frac{m}{k}$ (2) $π \frac{m}{2 k}$ (3) $2 π \frac{m}{k}$ (4) $2 π \frac{m}{2 k}$ 290. $A light hollow cube of side length 10 cm and mass 10 g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ \times 10^{- 2} s, where the value of y is (Acceleration due to gravity, g = 10 m / s^{2}, density of water = 10^{3} kg / m^{3})$ (1) $6$ (2) $2$ (3) $4$ (4) $1$ 291. $Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is$ (1) $\frac{π}{6}$ (2) $0$ (3) $\frac{2 π}{3}$ (4) $π$ 292. $Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E . The energy stored in B, when spring constants k_{A}, k_{B} of A and B, respectively satisfy the relation 4 k_{A} = 3 k_{B^{’}}, is :$ (1) $\frac{4}{3} E$ (2) $4 E$ (3) $3E$ (4) $2 E$ 293. $Y = Asin (ωt + φ_{0}) is the time - displacement equation of a SHM, At t = 0 the displacement of the particleis Y = \frac{A}{2} and it is moving along negative x - direction. Then the initial phase angle φ_{0} will be$ (1) $\frac{π}{6}$ (2) $\frac{π}{3}$ (3) $\frac{2 π}{3}$ (4) $\frac{5 π}{6}$ 294. $A particle executes simple harmonic oscillation with an amplitude a . The period of oscillation is T . The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is$ (1) $T /8$ (2) $T/12$ (3) $T /2$ (4) $T /4.$ 295. $When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:$ (1) $elliptical$ (2) $parabolic$ (3) $straight line$ (4) $circular$ 296. $In simple harmonic motion, the total mechanical energy of given system is E . If mass of oscillating particle P is doubled then the new energy of the system for same amplitude is:$ (1) $E$ (2) $E / 2$ (3) $2 E$ (4) $E 2$ 297. $A rod of mass ’ M ’ and length ’ 2 L ’ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of ' m' are attached at distance ’ L /2 ’ from its centre on both sides, it reduces the oscillation frequency by 20 % . The value of ratio m / M is close to$ (1) $0.77$ (2) $0.57$ (3) $0.37$ (4) $0.17$ 298. $A block of mass m is connected to a light spring of force constant k . The system is placed inside a damping medium of damping constant b . The instantaneous values of displacement, acceleration and energy of the block are x, a and E respectively. The initial amplitude of oscillation is A and ω^{'} is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is$ (1) $x = A e^{\frac{- b}{m}} cos (ω^{'} t + ϕ)$ (2) $ω^{'} = \frac{k}{m} - \frac{b ^{2}}{4 m ^{2}}$ (3) $E = \frac{1}{2} k A^{2} e^{- \frac{b t}{m}}$ (4) $m \frac{d ^{2} x}{d t ^{2}} + b \frac{d x}{d t} + k x = 0$ 299. $An electromagnetic wave of intensity enters in a medium of refractive index '' without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:$ (1) $(\frac{1}{n}, \frac{1}{n})$ (2) $\frac{F}{3 mR}$ (3) $(n, \frac{1}{n})$ (4) $(\frac{1}{n}, n)$ 300. $The time period of a simple harmonic oscillator is T = 2 π \frac{m}{k} . Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is____1% .$ (1) $7.60$ (2) $3.35$ (3) $3.43$ (4) $6.76$