circular motion

Q.1 A 10 kg ball attached to the end of a rigid massless rod of length 1 m rotates at constant speed in a horizontal circle of radius 0.5 m and period 1.57 sec as in fig. The force exerted by rod on the ball is (A) 1.28 N (B) 128 N (C) 10 N (D) 12.8 N Q.2 Two bodies A & B rotate about an axis, such that angle A (in radians) covered by first body is proportional to square of time, &B (in radians) covered by second body varies linearly. At t = 0, A = B = 0. If A completes its first revolution in  sec. & B needs 4 sec. to complete half revolution then; angular velocity A : B at t = 5 sec. are in the ratio (A) 4 : 1 (B) 20 : 1 (C) 80 : 1 (D) 20 : 4 Q.3 A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg. (A) 1 (B) 2 (C) 3 (D) 4 Q.4 Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point in its swing? (A) (B) (C) (D) Q.5 The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will (A) always be in contact with the inner wall of the tube (B) always be in contact with the outer wall of the tube (C) initially be in contact with the inner wall and later with the outer wall (D) initially be in contact with the outer wall and later with the inner wall Q.6 A hollow vertical cylinder of radius R is rotated with angular velocity  about an axis through its center. What is the minimum coefficient of static friction necessary to keep the mass M suspended on the inside of the cylinder as it rotates? (A)  = 2 gR  (B)  = Rg 2  (C)  = gR 2  (D)  = R g2  Q.7 A horizontal curve on a racing track is banked at a 45° angle. When a vehicle goes around this curve at the curve’s safe speed (no friction needed to stay on the track), what is its centripetal acceleration? (A) g (B) 2g (C) 0.5g (D) none Q.8 The dumbell is placed on a frictionless horizontal table. Sphere A is attached toa frictionless pivot so that B can be made to rotate about A with constant angular velocity. If B makes one revolution in period P, the tension in the rod is (A) 2 2 PMd 4 (B) 2 2 PMd 8 (C) PMd 4 2  (D) PMd 2 Q.9 Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle in the same time t. The ratio of the angular speeds of the first to the second car is (A) 1 : 1 (B) m1 : m2 (C) r1 : r2 (D) m1m2 : r1r2 Q.10 The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing? (A) (B) (C) (D) Q.11 Two particles move on a circular path (one just inside and the other just outside) with angular velocities  and 5 starting from the same point. Then (A) they cross each other at regular intervals of time  42 when their angular velocities are oppositely directed. (B) they cross each other at points on the path subtending an angle of 60oat the centre if their angular velocities are oppositely directed. (C) they cross at intervals of time  3 if their angular velocities are oppositely directed. (D) they cross each other at points on the path subtending 90o at the centre if their angular velocities are in the same sense. Q.12 A cart moves with a constant speed along a horizontal circular path. From the cart, a particle is thrown up vertically with respect to the cart (A) The particle will land somewhere on the circular path (B) The particle will land outside the circular path (C) The particle will follow an elliptical path (D) The particle will follow a parabolic path Question No. 13 to 15 (3 questions) A particle of mass m is released from a height H on a smooth curved surface which ends into a vertical loop of radius R, as shown Q.13 Choose the correct alternative(s) if H = 2R (A) The particles reaches the top of the loop with zero velocity (B) The particle cannot reach the top of the loop (C) The particle breaks off at a height H = R from the base of the loop (D) The particle break off at a height R < H < 2R Q.14 If  is instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical, then identify the correct statement(s) related to the normal reaction N between the block andthe surface (A) The maximum value N occurs at  = 0 (B) The minimum value of N occurs at N =  for H > 5R/2 (C) The value of N becomes negative for /2 <  < 3/2 (D) The value of N becomes zero only when   /2 Q.15 The minimum value of H required so that the particle makes a complete vertical circle is given by (A) 5 R (B) 4 R (C) 2.5 R (D) 2 R Q.16 A small particle of mass m is given an initial high velocity in the horizontal plane and winds its cord around the fixed vertical shaft of radius a. All motion occurs essentially in horizontal plane. If the angular velocity of the cord is 0 when the distance from the particle to the tangency point is r0, then the angular velocity of the cord  after it has turned through an angle  is (A)  = 0 (B)  = 00 r a (C)  = 0 0r a 1   (D)  = 0 Q.17 A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle which has twice its mass during the impact. (A) The minimum kinetic energy of the system is 1 joule. (B) The maximum elastic potential energy of the system is 2 joule. (C) Momentum and total kinetic energy of the system are conserved at every instant. (D) The ratio of kinetic energy to potential energy of the system first decreases and then increases. Q.18 A ball of mass m collides elastically with an identical ball at rest with some impact parameter. (A) 100 % energy transfer can never take place (B) 100 % energy transfer may take place (C) angle of divergence between the two balls must be 90° (D) angle of divergence between the two balls depend on impact parameter Q.19 Two balls A and B having masses 1 kg and 2 kg, moving with speeds 21 m/s and 4 m/s respectively in opposite direction, collide head on. After collision A moves with a speed of 1 m/s in the same direction, then correct statements is : (A) The velocity of B after collision is 6 m/s opposite to its direction of motion before collision. (B) The coefficient of restitution is 0.2. (C) The loss of kinetic energy due to collision is 200 J. (D) The impulse of the force between the two balls is 40 Ns. Q.20 An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object (A) (R/3, R/3) (B) (R/3, R/2) (C) (R/4, R/4) (D) ( 2 R , 2 R )ANSWER KEY Q.1 B Q.2 C Q.3 C Q.4 B Q.5 C Q.6 D Q.7 A Q.8 B Q.9 A Q.10 A Q.11 B,C,D Q.12 B,D Q.13 B,D Q.14 A,B,D Q.15 C Q.16 C Q.17 A,B,D Q.18 A,C Q.19 A,B,C Q.20 B,D