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IIT JEE Exam 2024 : physics

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Class DPP : 03 CIRCULAR MOTION 1. A particle is moving on a circular path. The angle turned by radius vector is = 0(1 e t/3), where is in radian and t is in second. The angular acceleration at t = 0 is 1) 1 rad/s2 3 3) 10 rad/s2 2) 1 rad/s2 9 1 4) rad/s2 6 2. A point P moves in a co unt er -cl ock wi se direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a length s = t3 + 5, where s is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when, t = 2 s is nearly, is 1) 13 ms 2 2) 12 ms 2 3) 7.2 ms 2 4) 14 ms 2 3. A particle P starts from rest with constant angular acceleration in anti-clockwise direction from point P on a circular path of radius R. The acceleration of the particle at t = RCC / is 1) R i R j 2) R k R j 3) R i R j 4) None of these RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** SINGLE CORRECT ANSWER TYPE 4. For a particle in a uniform circular motion, the acceleration a at a point P (R, on the circle of radius R is (here, is measured from the X-axis) 1) v2 v2 cos i sin j R R 2) v2 v2 sin i cos j R R 3) v2 v2 cos i sin j R R 4) v2 v2 i j R R 5. A small block of mass 10 g is fastened to one end of a light string and a second block m2 of mass 20 g to the middle point, the other end of the string fastened to a fixed point on a smooth horizontal table. The blocks are then projected such that the two portions of the string are always in the same straight line and the blocks describe horizontal circles on the table as shown in the figure below. The tension in string portion between blocks is T1 and tension between point O and the block T1 of mass m2 is T2. The value of T is 2 1) 1 3) 0.5 2) 2 4) 0.25 1 1) 2g a 2) 2g c 3) 2g b 4) 2 gc ab 9. The situation shown in figure, a ball of mass 2 kg connected to a vertical revolving rod by two light strings of length 2 m, each making an angle of 45 with the rod. Both the rod and ball are revolving with angular velocity of 10 rad/s. The tension in upper string is 1) 20 N 2) 40 N 3) 50 N 4) zero 10. A spotlight S rotates in a horizontal plane with constant angular-velocity of 0.1 rad/s. The spot of light P moves along the wall at a distance of 3 m. The velocity of the spot P when = 45 as shown in the figure is 1) 0.6 m/s 2) 6 m/s 3) 0.5 m/s 4) 5 m/s RCC RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** 6. A phonograph turntable rotates at constant angular velocity 5 rad/s. A coin is placed at distance 0.5 m from the centre of the phonograph. Find the minimum value of coefficient of static friction so that the coin does not slip over the phonograph. 1) 0.25 2) 0.5 3) 0.75 4) 0.8 7. A circular ring of mass 3.14 kg and radius 0.05 m is rotating with constant angular velocity 10 rad/s about its centre. The tension in the wire of ring is 1) 1 N 2) 2 N 3) 2.5 N 4) 5 N 8. A bead of mass m rests on a vertical smooth parabola x 2 = cy at ( a, b) as shown in the figure. The required value of angular velocity is 11. Two moving particles P and Q are 10 m apart at a certain instant. The velocity of P is 8 m/s making an angle of 30 with the line joining P and Q and that of Q is 6 m/s making an angle of 30 with PQ as shown in the figure. Then, angular velocity of P with respect to Q is 1) zero 2) 0.1 rad/s 3) 0.4 rad/s 4) 0.7 rad/s 12. A smooth wire bent in the form of parabola x2 = 4 by as shown in the figure. A particle is moving with speed of v0 = 2gb at the vertex. Find radius of curvature of vertex, if the normal reaction on the particle at the vertex is 2mg. 1) b 2) 2 b 3) 3 b 4) 4 b 13. A bug crawls at a constant rate v0 along the spoke of a bicycle wheel of radius R, the bicycle is moving with a speed u. Find the magnitude of component of acceleration along the spoke in the form of r, the distance from centre of wheel. 1) ru 2 R2 2) r v02 R2 r (u 2 v02 ) 4) None of these R2 14. A horizontal rectangular pipe is rotating with constant angular velocity of 5 rad/s. The vertical faces of the pipe are smooth but bottom face is rough. The coefficient of friction between bottom face and a block of mass 1 kg is = 0.5. Find the acceleration of the block relative to pipe, if it is at distance 1 m from the point O. 3) 1) 25 m/s 2 3) 20 m/s 2 2) 5 m/s2 4) 10 m/s 2 2 1) 2g l 2 2) g 2 3) g 2l 2 4) g l 2 ASSERTION REASONING TYPE These questions consist of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following responses. A. If both Assertion and Reason are True and the Reason is a correct explanation of the Assertion. B. If both Assertion and Reason are True but Reason is not a correct explanation of the Assertion. C. If Assertion is True but the Reason is False. D. If both Assertion and Reason are False. 16. Assertion : In decelerated circular motion, magnitude of acceleration is lesser than the magnitude of radial acceleration. Reason : The acceleration of the particle in the case of circular motion is found by resultant of radial acceleration and tangential acceleration. 17. Assertion : In an atom, an electron can move around the nucleus is two circular orbits of radii r and 4 r. The ratio of the times taken by it to complete one revolution in two orbits is 1 : 8 . Reason : Time period T and radius r of circular path of electron in case of atom is related as T2 r3. 18. Assertion : A particle is moving on a circular path with centripetal acceleration ar = 2t2. The motion of the particle is a uniform circular motion. Reason : In the case of a uniform circular motion, net force is always directed towards centre of the circular path. RCC RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** 15. A bug rests on vertical part BC of the frame ABC. The frame is rotating with constant angular velocity about ZZ'-axis. The length of portion AB of the wire is l. Find possible value of coefficient of static friction between the wire and bug so that bug does not slip over the wire. 19. Assertion : A particle of mass m begins to slide down a fixed smooth hemisphere from the lop. Its tangential acceleration is 5 g when it 3 breaks off the sphere. Reason : At the time of breaking the surface of hemisphere, acceleration of the particle is g. 20. Assertion : Two rings of radii R and r turning at angular velocities 1 and 2. Consider a particle A whose mass is m and is fixed at upper ring. The centrifugal force acting on the particle A observed from the frame of lower ring is mr 12 . Reason : Centrifugal force is a pseudo force. MATCHING COLUMN TYPE 21. Match the Column I with Column II and select the correct option from the given i ii iii iv. 1) 2) 3) 4) Column I Motion of a particle on circular path with increasing speed (v 0) Column II p. Acceleration is directed towards centre Motion of a car on circular Acceleration is not q. path with constant speed directed towards centre Motion of cyclist on circular path with decreasing speed (v 0) Motion of a particle on a circular path with constant angular acceleration i q,r i p,q, i p, i q,r, ii p,r, ii r,s, ii q, ii p,s r. Centripetal acceleration is non-zero s. Friction is not direced towards centre iii q,r,s, iii p, iii r, iii q,p, iv q,r iv s iv s iv q 3 22. A rough wire is bent into two circular parts of equal radius 1 m as shown in figure below. Each part is a quarter of circle. Points O and O are respective centres. A bug of mass 1 kg travels on the wire with constant speed v0 = 1 m/s. v0 Match the column I with Column II and select the correct option from the given codes. i. ii iii. iv. Column I Normal reaction in newton on bug at B Friction in newton on bug at D Normal reaction in newton on bug just before crossing the point C Minimum coefficient of friction between bug and the wire so that bug does not slip over the wire. Column II p. q. r. s. Zero (5 2 1) 10 10 2 11 1) i-s, ii-p, iii-q, iv-r 2) i-p, ii-q, iii-r, iv-s 3) i-q, ii-p, iii-s, iv-r 3) i-s, ii-r, p-iii, iv-q 23. A particle moves on a circular path of radius 7 m with constant speed 7 m/s. Match the Column I with Column II and mark the correct option given below. Column I The magnitude of displacement in metre of i. the particle during travelling the quarter of Column II p. 6.3 ii circle The magnitude of average velocity in m/s during q. 7 iii. travelling quarter of circle The magnitude of acceleration in m/s2 of the r. 2 s. 7 2 particle The magnitude of average iv. acceleration in m/s2 during travelling a quarter of circle 1) i-s, ii-p, iii-q, iv-p 3) i-q, ii-p, iii-s, iv-r RCC RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** RCC** INTEGER TYPE 24. A particle is moving on a circular path of radius 1 m. It starts from rest, its tangential acceleration is 3 t. The time after which the acceleration of the particle makes an angle of 30 with centripetal acceleration is (n)2/3 s. Find the value on n. 25. A bug is moving on horizontal circular path of radius R. It starts from rest with a tangential acceleration of constant magnitude a0. The coefficient of static friction between the bug and horizontal path is . The time after which the bug will skids is {R 2 ( 2 g 2 a02 )} 1 / n . Find the value of n. a0 2) i-p, ii-q, iii-r, iv-s 3) i-s, ii-r, p-iii, iv-q 4

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