Title 05. CIRCULAR MOTION ( 133 - 154 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 133 IIT ADVANCED JEE ADVANCED - VOL-II CIRCULAR MOTION NISHITH Multimedia India (Pvt.) Ltd., CIRCULAR MOTION LEVEL - V SINGLE ANSWER QUESTIONS 1. A bead of mass m moves on a rod it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a horizontal plane with an acceleration a0 in a direction forming angle  with the rod. The acceleration of bead with respect to rod is a0 (A) g sin  (B) (g + a0 ) sin (C) g sin  + a0 cos  (D) g sin  – a0 cos 2. A pendulum of mass m and length l is suspended from the ceiling of a trolley which has a constant acceleration a in the horizontal direction as shown in figure. Work done by the tension is (in the frame of trolley) a (A)  mgl1 cos (B) mal sin (C) mal cos (D) zero 3. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time as ac = k2 rt2 , where k is a constant. The power delivered to the particle by the forces acting on it is – (A) 2 mk2 r 2 t (B) mk2 r 2 t (C) 3 1 mk4 r 2 t 5 (D) 0 4. A smooth sphere of radius R is made to trans- late in a straight line with a constant accel- eration a = g. A particle kept on the top of the sphere is released from there at zero veloc- ity with respect to the sphere. The speed of the particle with respect to sphere as a func- tion of  as it slides down is (A) Rg(sin cos )    (B) Rg(1 cos sin )     (C) 4 sin Rg  (D) 2 (1 sin cos ) Rg     5. The figure shows the velocity and accelera- tion of a point like body at the initial mo- ment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is  0   150 2 a m s  4 / 0 v m s  8 / (A) 2 meter (B) 4 meter (C) 8 meter(D) 16 meter 6. A stone is thrown horizontally with a veloc- ity of 10m/sec. Find the radius of curvature of it’s trajectory at the end of 3 s after mo- tion began.  2 g m s 10 / (A)10 10 m (B)100 10 m (C) 10 m (D)100m 7. A section of fixed smooth circular track of radius r in vertical plane is shown in the fig- ure. A block is released from position x and leaves the track at y. The radius of curva- ture of its trajectory when it just leaves the track at y is X R O O Y 0 53 0 37 (A) r (B) 4 r (C) 2 r (D) none of these
Jr Chemistry E/M CIRCULAR MOTION 134 NISHITH Multimedia India (Pvt.) Ltd., NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-II 8. A small coin of mass 80g is placed on the horizontal surface of a rotating disc. The disc starts from rest and is given a constant an- gular acceleration 2   2 / rad s . The coef- ficient of static friction between the coin and the disc is 3 / 4 s  and coefficient of ki- netic friction is 0.5 k  . The coin is placed at a distance r m 1 from the centre of the disc. The magnitude of the resultant force on the coin exerted by the disc just before it starts slipping on the disc is Vertical r (A): 0.2 N (B) 0.3 N (C) 0.4 N (D) 1N 9. A circular road of radius R is banked for a speed v =40km/hr. A car of mass m attempts to go on the circular road, the friction co- efficient between the tyre and road is negli- gible. (A) the car cannot make a turn without skidding (B) if the car runs at a speed less than 40km/hr, it will slip up the slope. (C) if the car runs at the correct speed of 40km/ hr, the force by the road on the car is equal to 2 mv r/ (D) if the car runs at the correct speed of 40km/ hr, the force by the road on the car is greater than mg as well as greater than 2 mv r/ . 10. A ring of mass 2 kg and of radius 0.25m is making 10rad/s about an axis through is cen- tre perpendicular to its plane. The tension (in newtons) developed in the ring is (A) 25 (B) 100 (C)175 (D) 250 11. A car is moving with speed 10 3 / sec m on a circular path of radius 100m. Its speed is increasing at the rate of 2 4 / sec m . What is the acceleration of the car? (A) 2 4 / sec m (B) 2 5 / sec m (C) 2 9.8 / sec m (D) 2 40 3 / sec m 12. A table fan rotating at a speed of 2400rpm is switched off and the resulting variation of the rpm with time is shown in the fig. The total number of revolutions of the fan be- fore it comes to rest is (A) 420 (B) 280 (C) 190 (D) 16800 13. Two particles tied to different strings are whirled in a horizontal circle as shown in fig- ure. The ratio of lengths of the strings so that they complete their circular path with equal time periodi is  3 0 0   0 60 m L2 L1 m a b (A) 3 2 (B) 1 3 (C) 1 (D) 3
NISHITH Multimedia India (Pvt.) Ltd., 135 IIT ADVANCED JEE ADVANCED - VOL-II CIRCULAR MOTION NISHITH Multimedia India (Pvt.) Ltd., 14. A particle moves in a circle of radius 4cm clockwise at constant speed 2cm/sec. If xˆ and yˆ are unit acceleration vectors along x and y-axes respectively (in cm/sec2 ), the acceleration of the particle at the instant halfway between P and Q is given by Y O X P Q (A)   4 x y ˆ ˆ (B) 4 x y ˆ ˆ   (C)   1 ˆ ˆ 2  x y (D) x y ˆ ˆ   4 15. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity  . The force exerted by liquid on the other end is (A) 2 2 ML (B) 2 ML (C) 2 4 ML (D) 2 2 2 ML  16. A car is moving in a circular horizontal track of radius 10m with constant speed of 10m/ sec. A plumb line bob is suspended from the roof of the car by a light rigid rod of length 1.0m. The angle made by the rod with the track is (A) Zero (B) 0 30 (C) 0 45 (D) 0 60 MULTIPLE ANSWER QUESTIONS 17. Regarding a frame attached to the Earth which of the following statement is wrong (A) Is an inertial frame by definition (B) Cannot be an inertial frame because the Earth is revolving around the sun (C) is an inertial frame because Newton’s laws of motion are applicable in this frame (D) Cannot be inertial frame because the Earth is rotating about its own axis. 18. A particle is moving along a circular path of radius R such that radial acceleration of particle proportional to t2 then (A) Speed of particle is constant (B) Magnitude of tangential acceleration of particle is constant (C) Speed of particle is proportional to time (D) Magnitude of tangential acceleration is variable 19. A ball of mass m is rotating in a circle of radius r with speed v inside a smooth cone as shown in figure. Let N be the normal reaction on the ball by the cone, then choose the wrong option: (A) Ncos mg   (B) 2 v gsin cos r    (C) 2 mv Nsin 0 r    (D) None of these 20. A simple pendulum of length L and mass (bob) M is oscillating in a vertical plane be- tween angular limits  and  . For an an- gular dispalcement     (| | ) , the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions (A) Tcos Mg   (B) 2 MV T Mgcos L    (C) The magnitude of the tangential acceleration of the bob T | a | gsin   (D) T Mgcos  
Jr Chemistry E/M CIRCULAR MOTION 136 NISHITH Multimedia India (Pvt.) Ltd., NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL-II 21. In the system shown in the figure the mass m moves in a circular arc of angular ampli- tude 60o . Mass 4m is stationary . Then: m m 60o 4m A B (A) the minimum value of coefficient of friction between the mass 4m and the surface of the table is 0.50 (B) the work done by gravitational force on the block m is positive when it moves from A to B (C) the power developed by the tension when m moves from A to B is zero (D) The kinetic energy of m in position B equals the work done by gravitational force on the block when its moves from position A to B. 22. A pendulum is released from point A as shown in figure. At some instant net force on the bob is making an angle  with the string: A B C (A) for =90o particle is at A (B) for  =0o particle is at B (C) for  =90o particle released at the position where string is horizontal (D) For  = 0o particle is at A 23. A small block of mass m is released from rest from position A inside a smooth hemi- spherical bowl of radius R as shown in fig- ure. Choose the wrong option : A R B (A) acceleration of block is constant throughout (B) acceleration of block is g at A (C) acceleration of block is 3g at B (D) acceleration of block is 2g at B. 24. A small ball is connected to a block by light string of length l. Both are initially on the ground. There is sufficient friction on the ground. There is sufficient friction on the ground to prevent the block from slipping. The ball is projected vertically up with a velocity u, where 2gl < u 2 < 3gl. The center of mass of the ‘block + ball’ system is C u (A) C will move along a circle (B) C will move along a parabola (C) C will move along a straight line (D) The horizontal component of the velocity of the ball will first increase and then decrease. 25. An object follows a circular path. The fol- lowing quantities may remain constant dur- ing motion (A) speed (B) velocity (C) acceleration (D) magnitude of acceleration 26. A particle is describing circular motion in a horizontal plane in contact with the smooth inside surface of a fixed right circular cone with its axis vertical and vertex down. The height of the plane of motion above the ver- tex is h and the semivertical angle of the cone is  . The period of revolution of the particle.  h (A) Increases as h increases (B) Decreases as h increases (C) Increases as  increases (D) Decreases as  increases