Physics-3.Unit-6 Test

UNIT–06 TEST 1. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved? (A) centre of the circle (B) on the circumference of the circle. (D) inside the circle (D) outside the circle 2. A horizontal circular plate is rotating about a vertical axis passing through its centre with an angular velocity ω0. A man sitting at the centre having two blocks in his hands stretches out his hands so that the moment of inertia of the system doubles. If the kinetic energy of the system is K initially, its final kinetic energy will be (A) 2K (B) K/2 (C) K (D) K/4 3. A disc is rolling without slipping with angular velocity ω. P and Q are two points equidistant from the centre C. The order of magnitude of velocity is (A) vQ > vC > vP (B) vP > vC > vQ (C) vP = vC, vQ = vC/2 (D) vP < vC > vQ 4. A uniform thin rod of mass M and length L is standing vertically along the Y–axis on a smooth horizontal surface with its lower end at origin (0, 0). A slight disturbance at t = 0 causes the lower end to slip on smooth surface along the positive X–axis and the rod starts falling. The path followed by the centre of mass of the rod during its fall is a/an. (A) Straight line (B) Parabola (C) Ellipse (D) Circle 5. A spinning ballet dancer changes the shape of her body by spreading her arms. (A) The angular momentum of the system is conserved. (B) The angular velocity of the system increases. (C) The rotational kinetic energy of the system increases. (D) The moment of inertia of the system decreases. 6. A uniform disc of mass M object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is. (A) (B) (C) (D) 7. A spool with a thread wound on it is placed on a smooth inclined plane set at an angle of 30° to the horizontal. The free end of the thread is attached to the wall as shown. The mass of the spool is m = 200g, its moment of inertia relative to its own axis is I = 0.45gm2, the radius of the wound thread layer is r = 3 cm. The acceleration of the spool axis is: (A) 0.5ms – 2 (B) 5 ms – 2 (C) 1.4 ms – 2 (D) 14ms – 2 8. A thin rectangular plate with sides of length a and b has mass per unit area varying as where is a constant. The centre of mass co–ordinates of the plate are. (A) (B) (C) (D) 9. A hemisphere and a solid cone have a common base. The centre of mass of the common structure coincides with the centre of the common base. If R is the radius of hemisphere and h is height of the cone, then. (A) (B) (C) (D) 10. A bar of mass m, length is in pure translatory motion with its centre of mass velocity . It collides with and sticks to another identical bar at rest as shown in figure. Assuming that after collision it becomes one composite bar of length 2l, the angular velocity of the composite bar will be. (A) , anticlockwise (B) , anticlockwise (C) , clockwise (D) , clockwise 11. 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 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) (B) (C) (D) 12. A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration . If the coefficient of friction between rod and the bead is , and gravity is neglected, then the time after which the bead starts slipping is. (A) (B) (C) (D) infinitesimal 13. Each of the three balls has a mass m and is welded to the rigid equiangular from of negligible mass. The assembly rests on a smooth horizontal surface. A force F is suddenly applied to one bar as shown. (A) Acceleration of point O is (B) Acceleration of point O is (C) The magnitude of angular acceleration of the frame is (D) The magnitude of angular acceleration of the frame is 14. Ring of mass 6 kg and radius 40 cm is revolving at the rate of 300 revolutions per minute. Its moment of inertia will be (A) 0.92 kg m2 (B) 0.96 kg m2 (C) 2.4 kg m2 (D) 2.98 kg m2 15. Ring of mass 6 kg and radius 40 cm is revolving at the rate of 300 revolutions per minute. Its kinetic energy of rotation of ring is (A) joule (B) joule (C) joule (D) joule 16. Let IA and IB be moment of inertia of a body about two axes A and B respectively. The axis A passes through the centre of mass of the body but B does not (A) IA

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