Physics-DPP-3-Rotational Motion

PHYSICS Topic: ROTATIONAL MOTION Date: 1. A sphere of radius R is rolling on a rough horizontal surface. The magnitude of velocity of A with respect to ground will be : (a) 2vCM (b) 2vCM sin θ (c) 2vCM (d) no sufficient information. 2. In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity v0. The radius and angular velocity of the sphere is r and ω respectively. The velocity of centre of mass of the sphere is (a) v0 + rω (b) v0 – rω (c) rω (d) v0 3. An imperfectly rough sphere moves from rest down a plane inclined at an angle α to the horizontal. The coefficient of friction between the inclined plane and sphere is μ . Then (a) if μ < 2 7 tan α , then the sphere never rolls (b) if μ = 2 tan α , then the maximum friction always being exerted. 7 (c) μ > 2 tan α , then pure rolling takes place (d) all of the above 7 4. Two rods OA and OB of equal length and mass are lying on xy plane as shown in figure. Let Ix, Iy and Iz be the moment of intertias of both the rods about x, y and z axis respectively, then : (a) Ix = Iy > Iz (b) Ix = Iy < Iz (c) Ix > Iy > Iz (d) Iz > Iy > Ix 5. A forces F is applied on the top of a cube as shown in figure. The coefficient of friction between cube and ground is μ . If F is gradually increased, the cube will topple before sliding if : (a) μ > 1 (b) μ < 1 2 (c) μ > 1 2 (d) μ < 1 PHYSICS Topic: ROTATIONAL MOTION Date: 6. A disc is rolling (without slipping on a horizontal surface) on a horizontal surface with C as its centre and Q and P the two points equidistance from C. Let vP, vQ and vC be the magnitude of velocities of points P, Q and C respectively, then : (a) vQ > vC > vP (b) vQ < vC < vP (c) 1 vQ = vP , vC = 2 vP (d) vQ < vC > vP 7. A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin : (a) is zero (b) remains constant (c) goes on increasing (d) goes on decreasing 8. When a body is projected at an angle with the horizontal in the uniform gravitational field of the earth, the angular momentum of the body about the point of projection, as it proceeds along its path : (a) remains constant (b) increases (c) decreases (d) initially decreases and increases after its highest point 9. A uniform rod OA of mass M and length 2a rests on a smooth table and is free to turn about a smooth pivot at its end O, in contact with it at a distance b from O is an inelastic particle of mass m. A horizontal blow of impulse p is given to rod at a distance x from O in a direction perpendicular to the rod. The resultant instantaneous angular velocity of the rod is : (a) px 4Ma2 + mb px (b) M (c) px ma2 + mb2 πp (d) ml 3 10. A uniform rod AB of mass m and length l is at rest on a smooth horizontal surface. An impulse p is applied to the end B. The time taken by the rod to turn through a right angle is : (a) 2π ml p (b) 2π p ml (c) πml 12 p πp (d) ml PHYSICS Topic: ROTATIONAL MOTION Date: 1. (c) 2. (a) Answer Key 3. (d) 4. (b) 5. (c) 6. (a) 7. (b) 8. (b) 9. (a) 10. (c)