Simple Harmonic Motion PYQs Set 10 (PDF)

Set 10 of 13 · Questions 271-300 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 10 (Q271-300)
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271. $Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge q_{0} with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q_{0} executes SHM. The time period of oscillation of charge q_{0} will be:$ (1) $\frac{4 π ^{3} ϵ _{0} m a ^{3}}{q _{0} Q}$ (2) $\frac{q _{0} Q}{4 π ^{3} ϵ _{0} m a ^{3}}$ (3) $\frac{2 π ^{2} ϵ _{0} m a ^{3}}{q _{0} Q}$ (4) $\frac{8 π ^{2} ϵ _{0} m a ^{3}}{q _{0} Q}$ 272. $For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is ω_{1} . When the mass block is 2 kg the angular frequency is ω_{2} . The ratio ω_{1} / ω_{2} is:$ (1) $2$ (2) $\frac{1}{2}$ (3) $2$ (4) $\frac{1}{2}$ 273. $A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x_{1} (t) = A sin ꞷt and x_{2} (t) = A sin (ωt + \frac{2 π}{3}) . Adding a third sinusoidal displacement x_{3} (t) = B sin (ꞷt + ɸ) brings the mass to a complete rest. The values of B and ɸ are$ (1) $2 A, \frac{3 π}{4}$ (2) $A, \frac{4 π}{3}$ (3) $3 A, \frac{5 π}{6}$ (4) $A, \frac{π}{3}$ 274. $A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is x = \frac{A}{2} and it moves along positive x-axis. The displacement of particle in time t is x = A sin (ωt + δ), then the value 8 will be$ (1) $\frac{π}{2}$ (2) $\frac{π}{6}$ (3) $\frac{π}{3}$ (4) $\frac{π}{4}$ 275. $As shown in the figure, a block of weight 20 N is connected to the top of a smooth inclined plane bymassless spring of constant 8 π^{2} Nm^{- 1} . If the block is pulled slightly from its mean position and released, the period of oscillations is(Acceleration due to gravity = 10 ms^{- 2})$ (1) $4 s$ (2) $3 s$ (3) $2 s$ (4) $1 s$ 276. $For a particle executing simple harmonic motion, the displacement-time (x - t) graph is as shown in the figure. The acceleration of the particle at t = \frac{4}{3} s is$ (1) $- \frac{3}{32} π^{2} cm s^{- 2}$ (2) $\frac{32}{3} π^{2} cm s^{- 2}$ (3) $+ \frac{3}{32} πcm s^{- 2}$ (4) $+ \frac{32}{3} πcm s^{- 2}$ 277. $A cone with half the density of water is floating in water as shown in figure. It is depressed down by a small distance δ (< H) and released. The frequency of simple harmonic oscillations of the cone is$ (1) $\frac{1}{2 π} \frac{6 g}{H} \frac{1}{4 ^{\frac{1}{3}}}$ (2) $\frac{1}{2 π} \frac{3 g}{H} \frac{1}{4 ^{\frac{1}{3}}}$ (3) $\frac{1}{2 π} \frac{6 g}{H}$ (4) $\frac{1}{2 π} \frac{g}{H}$ 278. $A simple pendulum oscillating in air has period T . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is \frac{1}{16} th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:$ (1) $2 T \frac{1}{10}$ (2) $2 T \frac{1}{14}$ (3) $4 T \frac{1}{15}$ (4) $4 T \frac{1}{14}$ 279. $A simple pendulum of length ' l' and a bob of mass ' m' is executing S.H.M. of small amplitude ' A'. The maximum tension in the string will be (g = acceleration due to gravity)$ (1) $2 mg$ (2) $mg (1 + (\frac{A}{l})^{2})$ (3) $mg (1 + (\frac{A}{l}))^{2}$ (4) $mg (1 + (\frac{A}{l}))$ 280. $A particle executing SHM along a straight line has zero velocity at points A and B whose distance from O on the same line OAB are a and b, respectively. If the velocity at the mid point between A and B is v, then its time period is$ (1) $\frac{π ( b + a )}{v}$ (2) $π (\frac{b - a}{v})$ (3) $(\frac{b + a}{2 v})$ (4) $(\frac{b - a}{2 v})$ 281. $Two particle are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is:$ (1) $0$ (2) $2π/3$ (3) $π$ (4) $π/6$ 282. $A pendulum is oscillating at a frequency of 8 Hz . Suddenly the string of the pendulum is clamped at its midpoint then the new frequency of oscillations is$ (1) $16 Hz$ (2) $13.8 Hz$ (3) $11.28 Hz$ (4) $5.7 Hz$ 283. $A bead of mass m stays at point P (a, b) on a write bent in the shape of a parabola y = 4 C x^{2} and rotating with angular speed ω (see figure). The value of ω is (neglect friction)?$ (1) $2 2 gc$ (2) $2 gc$ (3) $\frac{2 g}{C}$ (4) $\frac{2 gC}{ab}$ 284. $A straight rod of length L extends from x = a to x = L + a . The gravitational force it exerts on point mass ' m ’ at x = 0, if the mass per unit length of the rod is A + B x^{2}, is given by:$ (1) $Gm [A (\frac{1}{a + L} - \frac{1}{a}) - BL]$ (2) $Gm [A (\frac{1}{a} - \frac{1}{a + L}) - BL$ (3) $Gm [A (\frac{1}{a + L} - \frac{1}{a}) + BL]$ (4) $Gm [A (\frac{1}{a} - \frac{1}{a + L}) + BL]$ 285. $A mass is suspended separately by two different springs in successive order then time periods is t_{1} and t_{2} respectively. If it is connected by both spring as shown in figure then time period is t_{0}, the correct relation is$ (1) $t_{0}^{2} = t_{1}^{2} + t_{2}^{2}$ (2) $t_{0}^{- 2} = t_{1}^{- 2} + t_{2}^{- 2}$ (3) $t_{0}^{- 1} = t_{1}^{- 1} + t_{2}^{- 1}$ (4) $t_{0} = t_{1} + r_{2} .$ 286. $A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m (in kg) is [NEET 2016]$ (1) $\frac{3}{4}$ (2) $\frac{4}{3}$ (3) $\frac{16}{9}$ (4) $\frac{9}{16}$ 287. $The distance covered by a particle undergoing SHM in one time period is (amplitude = A) [NEET 2019]$ (1) $zero$ (2) $A$ (3) $2 A$ (4) $4 A$ 288. $A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N / m . What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m / s^{2}) .$ (1) $10.0 cm$ (2) $any value less than 12.0 cm$ (3) $4.0 cm$ (4) $8.0 cm.$ 289. $In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. Thefree ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency ofoscillation of given body is:$ (1) $\frac{1}{2 π} \frac{2 k}{Mgsin α}$ (2) $\frac{1}{2 π} \frac{k}{Mgsin α}$ (3) $\frac{1}{2 π} \frac{2 k}{M}$ (4) $\frac{1}{2 π} \frac{k}{2 M}$ 290. $Two springs of spring constant k_{1} and k_{2} are connected by a mass m as shown in the figure. Under negligible friction, if the mass is displaced by small amount x from its equilibrium position and released, the period of oscillation is$ (1) $2 π \frac{m ( k _{1} + k _{2} )}{k _{1} k _{2}}$ (2) $2 π \frac{m}{k _{1} + k _{2}}$ (3) $2 π \frac{m k _{1} k _{2}}{( k _{1} + k _{2} )}$ (4) $2 π \frac{m ( k _{1} - k _{2} )}{k _{1} k _{2}}$ 291. $A uniform circular disc of mass 12 kg is held by two identical springs. When the dise is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take π^{2} = 10)$ (1) $230 N m^{- 1}$ (2) $120 N m^{- 1}$ (3) $60 N m^{- 1}$ (4) $30 Nm^{- 1}$ 292. $A particle is executing simple harmonic motion with a time period T. At time = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like:$ (1) (2) (3) (4) 293. $A particle is subjected to two simple harmonic motions as: x_{1} = 7 sin 5 tcm and x_{2} = 27 sin (5 t + \frac{π}{3}) cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is x \times 10^{- 2} ms^{- 2} . The value of x is:$ (1) $57$ (2) $125$ (3) $257$ (4) $175$ 294. $A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k . The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is:$ (1) $\frac{2 F}{mk}$ (2) $\frac{F}{π mk}$ (3) $\frac{πF}{mk}$ (4) $\frac{F}{mk}$ 295. $As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3s, then the period of oscillation in figure (b) will be x s . The value of x is_________.$ 296. $The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5 x s . The value of x will be________.$ 297. $In the reported figure, two bodies A and B of masses 200g and 800g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be rad/s when k=20N/m$ 298. $The time period of simple harmonic motion of mass M in the given figure is π \frac{αM}{5 K}, where the value of α is_______$ 299. $Time period of a simple pendulum is T . The time taken to complete \frac{5}{8} oscillations starting from mean positionis \frac{α}{β} T . The value of α is$ 300. $A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to covera displacement equal to half of its amplitude from the mean position is \frac{1}{a} S . The value of ’ a ’ to the nearestinteger is______$