Tiêu đề 03C.SHM-PHY LEVEL - VI ( 131 - 148 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 131 JEE ADVANCED - VOL - III JEE MAINS - CW - VOL - I SHM NISHITH Multimedia India (Pvt.) Ltd., LEVEL - VI SINGLE ANSWER QUESTIONS 1. The displacement - time graph of a particle executing SHM with a time period T has been shown in following fig. Four points 1, 2, 3 & 4 are marked on the graph where the displacement is half of the amplitude. The phase difference between the points which have the same displacement but move in opposite direction is........... (A) 3  (B) 2 3  (C) 2  (D)  2. The phase difference between the particles A,B which move according to equations 1 y t  3sin and y t t 2    4sin / 2 3sin          is (A) 1 4 tan 3        (B) 1 4 tan 5        (C) 1 3 tan 5        (D)  / 2 3. Two light springs of force constants 1 2 k k, and a block of mass m are in the line AsB on a smooth horizontal table such that one end of each spring is fixed on rigid upports and the other end is free as shown: The givenvalues are k N m k N m 1 2   1.8 / ; 3.2 / ; m gm L cm   200 ; 60 ; If the block moves along AB with a velocity 120 cm/sec in between the springs, then period of oscillation of the block is...................[ assume all collisions are elastic]: (A) 1.04 sec (B) 0.785 sec (C) 1 sec (D) 2.82 sec 4. The following figure shows a particle of mass, m , attached with four identical springs, each of length l . Initial tension in each spring is F0 . The period of small oscillations of the particle along a line perpendicular to the plane of the figure is..............[ neglect gravity] (A) 0 ml F  (B) 0 2 ml F  (C) 0 2 2 ml F  (D) 0 4 ml F  5. A V - shaped glass tube of uniform cross- section is kept in a vertical plane as shown. The angular frequency of small oscillations of liquid in a tube is................... (A) g sin .sin h   (B) g sin .sin h   (C) g h (D) g sin sin  h   
SHM 132 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - III NISHITH Multimedia India (Pvt.) Ltd., 6. A L - shaped bar of mass M is pivoted at one of its end so that it can freely rotate in a vertical plane as shown. If it is slightly displaced from its equilibrium position then the frequency of oscillation is.... (A) 1 3 10 2 4 g  L       (B) 1 10 2 4 g  L       (C)   1 2 2 g  L (D) 1 2 2 g  L 7. A uniform cylinder of mass m and radius R is in equilibrium on an inclined plane by the action of a light spring of stiffness k , gravity and reaction force acting on it. If the angle of inclination of the plane is  , then angular frequency of small oscillations of the cylinder is............... (A) 2 k m (B) 2 2 k m (C) 2 2 3 k m (D) 2k m 8. A body A of mass m1 and body B of mass m2 are interconnected by a massless spring as shown. The body A performs free vertical harmonic oscillations with the amplitude A and frequency f . The maximum value of f such that body B does not leave the surface is (A) 1 2 2 1 2 m m g  m A        (B) 1 2 1 1 2 m m g  m A        (C) 1 2 g  A (D) 2 1 1 . 2 m g  m A 9. In the arrangement shown, the sleeve of mass M is fixed between two identical springs whose combined force constant is k . The sleeve can slide without friction over a horizontal bar AB. The arrangement rotates with a constant angular velocity  about a vertical axis passing through the middle of the bar. The period of small oscillations of the sleeve is.............. (A) 2 m k  (B) 2 2 m k m    (C) m k  (D) 2 m k m   
NISHITH Multimedia India (Pvt.) Ltd., 133 JEE ADVANCED - VOL - III JEE MAINS - CW - VOL - I SHM NISHITH Multimedia India (Pvt.) Ltd., 10. A vertical pole of length l , density  , area of cross section A floats in two immiscible liquids of densities 1 2   and . In equilibrium position the bottom end is at the interface of the liquids. When the cylinder is displaced vertically, the time period of oscillation is............... (A)  1 2  l g      (B ) 1 2 l 1 1 g            (C)  1 2 l g      (D)  1 2  l g      11. A uniform rod of mass, m , and length l remains in equilibrium inside a smooth hemisphere of radius R as shown. The period of small oscillations of the rod is.... 2 2 2   r R l   / 4    (A) 2 2 12 2 l r gr   (B) 2 2 4 2 l r gr   (C) 2 R g  (D) 2 l R g   12. A thin uniform vertical rod of mass m and length l pivoted at point O is shown in Fig. The combined stiffness of the springs is equal to k . The mass of the spring is negligible. The frequency of small oscillation is (A) 3 2 k g m l  (B) 3 3 2 k g m l  (C) 3 3 2 k g m l  (D) 3 2 3 k g m l  13. A thin-walled tube of mass m and radius R has a rod of mass m and very small cross section soldered on its inner surface. The side-view of the arrangement is as shown The entire arrangement is placed on a rough horizontal surface. The system is given a small angular displacement from its equilibrium position, as a result, the system performs oscillations. The time period of resulting oscillations if the tube rolls without slipping is (A) 4 2 R g  (B) 2 2 R g  (C) 2 R g  (D) None of these
SHM 134 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - III NISHITH Multimedia India (Pvt.) Ltd., 14. A wire is bent at an angle  . A rod of mass m can slide along the bended wire without friction as shown in Fig. A soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is (A) 2 l g  (B) cos 2 l g   (C) 2 cos l g   (D) 2 tan l g   15. An elastic string of constant k is attached to a block of mass m as shown. The block is given an extension of 2mg k from the equilibrium position and released. The time period of oscillations of the block is (A) 2 m k  (B) 4 3 3 m k         (C) 2 2 3 m m k k   (D) 3 m m k k   16. A ship reaches the entrance to a harbor at noon. The depth of water over the harbor bar is 4 meter at low tide and 10 meter at high tide. Low tide is at 11.20 am and high tide is at 5.40 pm. Assume water surface moves in S.H.M. The ship requires a depth of 9.4 meter. The earliest time at which the ship can cross the harbor bar so as to reach the harbor is......[   1 Sin 0.8 53.13    ] (A) 4.23 pm (B) 1.53 pm (C) 2.30 pm (D) 3.13 pm 17. A ring of mass m can freely slide on a smooth vertical rod. The ring is symmetrically attached with two springs, as shown, each of stiffness k . Ring is displaced such that each spring makes an angle  with the horizontal. If the ring is slightly displaced vertically, then time period is............ (A) 2 m k  (B) sin 2 2 m k   (C) 2 sin 2 m k   (D) sin 2 m k   18. A light inextensible string carrying a spring is passed over two smooth fixed pulleys as shown. If the rod is slightly displaced about the hinge from is equilibrium position, then time period is. (A) 4 2 3 2 3 ml l kl mg    (B) 2 2 2 3 ml l kl mg     (C) 3 2 3 ml l kl mg     (D) 4 2 3 ml l kl mg    