Title 14.OSCILLATIONS - Questions.pdf ✅

14.OSCILLATIONS (1.)Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06π m and force constant 0.1N/m. Initially both the balls are displaced by an angle θ = π/6 radian with respect to the diameter PQ of the circle and released from rest. The frequency of oscillation of the ball B is (a.) π Hz (b.) 1 π Hz (c.) 2π Hz (d.) 1 2π Hz (2.)For any S.H.M. amplitude is 6 cm. If instantaneous potential energy is half the total energy then distance of particle from its mean position is (a.) 3 cm (b.) 4.2 cm (c.) 5.8 cm (d.) 6 cm (3.)Two springs of constant k1 and k2 are joined in series. The effective spring constant of the combination is given by (a.) √k1k2 (b.) (k1 + k2)/2 (c.) k1 + k2 (d.) k1k2/(k1 + k2) (4.)The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is (a.) 0.5 π (b.) π (c.) 0.707π (d.) Zero (5.)A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio of 1:2. What is the force constant of second piece in terms of k? (a.) k 2 (b.) 2k 2 (c.) 3k 2 (d.) 4k 2 (6.)If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ′b′ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds (a.) 0.693/b (b.) b (c.) 1/b (d.) 2/b (7.)Two simple harmonic motions of angular frequency 100 and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is (a.) 1:10 (b.) 1: 102 (c.) 1: 103 (d.) 1: 104 (8.)A girl swings on cradle in a sitting position. If she stands what happens to the time period of girl and cradle? (a.) Time period decreases (b.) Time period increases (c.) Remains constant (d.) First increases and then remains constant (9.)A weightless spring of length 60 cm and force constant 200 N/m is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of 0.25 kg is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is (a.) π 20 s (b.) π 10 s (c.) π 5 s (d.) π √200 s (10.)What will be the force constant of the spring system shown in figure? /6 /6
(a.) k1 2 + k2 (b.) [ 1 2k1 + 1 k2 ] −1 (c.) 1 2k1 + 1 k2 (d.) [ 2 k1 + 1 k2 ] −1 (11.)A particle doing simple harmonic motion, amplitude = 4 cm, time period = 12 s. The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is (a.) 1 (b.) 1/3 (c.) 1/4 (d.) 1/2 (12.)The springs shown are identical. When A = 4kg, the elongation of spring is 1 cm. If B = 6kg, the elongation produced by it is (a.) 4 cm (b.) 3 cm (c.) 2 cm (d.) 1 cm (13.)Two identical pendulum are oscillating with amplitudes 4 cm and 8 cm. the ratio of their energies of oscillation will be (a.) 1/3 (b. ) 1⁄4 (c.) 1⁄9 (d. ) 1⁄2 (14.)A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes angle of 60° with the vertical. The new reading of the balance is (a.) 10√3 kg wt (b.) 20√3kg wt (c.) 20 kg wt (d.) 10 kg wt (15.)A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y x is (a.) 4 (b.) 2 (c.) 1 2 (d.) 1 4 (16.)The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be (a.) 18 J (b.) 10 J (c.) 12 J (d.) 2.5 J (17.)To make the frequency double of a spring oscillator, we have to (a.) Reduce the mass to one fourth (b.) Quardruple the mass (c.) Double of mass (d.) Half of the mass (18.)The displacement y of a particle executing periodic motion is given by y = 4 cos2(t/ 2) sin(1000t). This expression may be considered to be a result of the superposition of........ independent harmonic motions (a.) Two (b.) Three (c.) Four (d.) Five (19.)A small block is connected to one end of a massless spring of un-stretched length 4.9m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2m and released from rest at B K K A K
t = 0. It then executes simple harmonic motion with angular frequency ω = π 3 rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P is at angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1s, the value of v is (take g = 10m/s 2 ) (a.) √50m/s (b.) √51m/s (c.) √52m/s (d.) √53m/s (20.)A pendulum of length 1 m is released from θ = 60°. The rate of change of speed of the bob at θ = 30° is (g = 10 ms −2 ) (a.) 10 ms −2 (b.) 7.5 ms −2 (c.) 5 ms −2 (d.) 5√3 ms −2 (21.)The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minute will be 1 X times the original, where X is (a.) 2 × 3 (b.) 2 3 (c.) 3 2 (d.) 3 × 2 2 (22.)A particle of mass m is executing oscillations about the origin on the x-axis with amplitude A. Its potential energy U(x) = ax 4 where a is positive constant. The x-coordinate of mass where potential energy is one-third of the kinetic energy of particle is (a.) ±A √3 (b.) ±A √2 (c.) ±A 3 (d.) ±A 2 (23.)When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm. by suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released, the maximum velocity in it (in ms −1 ) is (acceleration due to gravity=10 ms −2 ) (a.) 0.5 (b.) 1 (c.) 2 (d.) 4 (24.)A particle is subjected simultaneously to two SHM’s one along the x-axis and the other along the y-axis. The two vibrations are in phase and have unequal amplitudes. The particle will execute (a.) Straight line motion (b.) Circular motion (c.) Elliptic motion (d.) Parabolic motion (25.)Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system. Then the angular frequency of oscillation of m2 is (a.) √k/m1 (b.) √k/m2 (c.) √k/(m1 + m2) (d.) √k/(m1 − m2) (26.)Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system. The amplitude of oscillations is (a.) m1g k (b.) m2g k (c.) (m1+m2)g k (d.) (m1−m2)g k (27.)Mark the wrong statement (a.) All S.H.M.’s have fixed time period (b.) All motions having same time period are S.H.M. (c.) In S.H.M. total energy is proportional to square of amplitude (d.) Phase constant of S.H.M. depends upon initial conditions (28.)The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is
(a.) π 5 s (b.) 2π s (c.) 20π s (d.) 5π s (29.)A simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in horizontal position from the wall and is left free to move. The bob hits on the wall the coefficient of restitution is 2 √5 . After how many collisions the amplitude of vibration will become less than 60° (a.) 6 (b.) 3 (c.) 5 (d.) 4 (30.)The velocity of a particle performing simple harmonic motion, when it passes through its mean position is (a.) Infinity (b.) Zero (c.) Minimum (d.) Maximum (31.)A particle is moving in a circle with uniform speed. Its motion is (a.) Periodic and simple harmonic (b.) Periodic but no simple harmonic (c.) A periodic (d.) None of the above (32.)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 slightly and released the mass executes a simple harmonic motion. The spring constant is 200 Nm−1 . What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? (Take g=10 ms −2 ) (a.) 8.0 cm (b.) 10.0 cm (c.) Any value less than 12.0 cm (d.) 4.0 cm (33.)If the displacement equation of a particle be represented by y = A sinPT + B cos PT, the particle executes (a.) A uniform circular motion (b.) A uniform elliptical motion (c.) A S.H.M. (d.) A rectilinear motion (34.)A particle free to move along the x-axis has potential energy given as U(x) = k[1 − exp(−x 2)] (for − ∞ ≤ +∞) Where k is a positive constant of appropriate dimensions. Then (a.) At points away from origin, the particle is in equilibrium (b.) For any finite non-zero value of x, there is a force directed away from the origin (c.) Its total mechanical energy is k/2 and it is equal to its kinetic energy at origin (d.) At x = 0, the motion of the particle is simple harmonic (35.)A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by T = 2π√ 1 g′ , where g′ is equal to (a.) g (b.) g − a (c.) g + a (d.) √g2 + a 2 (36.)Two identical springs of constant K are connected in series and parallel as shown in figure. A mass m is suspended from them. The ratio of their frequencies of vertical oscillations will be (a.) 2 :1 (b.) 1 :1 (c.) 1 :2 (d.) 4 :1 (37.)The P.E. of a particle executing SHM at a distance x from its equilibrium position is (a.) 1 2 mω 2x 2 (b.) 1 2 mω 2a 2 (c.) 1 2 mω 2 (a 2 − x 2 ) (d.) Zero (38.)Two simple pendulums of lengths 1.44 m and 1 m start swinging together. After how m K K (B) m K K (A)