Tiêu đề 6-rotational-motion-.pdf ✅

Rotational Motion 1. Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with same speed v along parallel lines. At a particular instant, r1 and r2 are their respective position vectors drawn from point A which is in the plane of the parallel lines. Choose the correct options : (A) Angular momentum l1 of particle 1 about A is l = mvd1 ⊙ (B) Angular momentum l1 of particle 2 about A is l2 = mvr2 ⊙ (C) Total angular momentum of the system about A is l = mv(r1 + r2 ) ⊙ (D) Total angular momentum of the system about A is l = mv(d2 − d1 ) ⊗ ⊙ represents a unit vector coming out of the page. ⊗ represents a unit vector going into the page. 2. Two thin discs, each of mass M and radius r, are attached as shown in the figure, to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is : (A) 2Mr 2 (B) 3Mr 2 (C) 4Mr 2 (D) 5Mr 2 3. A circular hoop of mass m and radius R rests flat on a horizontal frictionless surface. A bullet, also of mass m, and moving with a velocity v, strikes the hoop and gets embedded in it. The thickness of the hoop is much smaller than R. The angular velocity with which the system rotates after the bullet strikes the hoop is : (A) V 4R (B) V 3R (C) 2V 3R (D) 3V 4R 4. Moment of inertia of the semicircular ring of mass M and radius R about an axis AB as shown in the figure. (A) dependent of angle θ (B) independent of angle θ (C) MR 2 , if θ = 45∘ (D) Mr 2 , if θ = π 2 5. The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it? (A) The forces may be acting radically from a point on the axis (B) The force may be acting on the axis of rotation (C) The force may be acting parallel to the axis
of rotation (D) The torque caused by some forces may be equal and opposite to that caused by other forces 6. From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is : (A) 4MR 2 (B) 40 9 MR 2 (C) 10MR 2 (D) 37 9 MR 2 7. Figure shows a lamina in x − y plane. Two axes z and z ′ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following are true? (The point P is closer to z ′ -axis than the z-axis.) (A) Torque τ caused by F about z axis is along −kˆ (B) Torque τ caused by F about z ′ axis is along −kˆ (C) Torque τ caused by F about τ axis is greater in magnitude than that about z axis (D) Total torque is given be τ = τ + τ ′ 8. Four identical rods, each of mass m and length l are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about (A) The x-axis is 2 3 ml 2 (B) The z-axis is 4 3 ml 2 (C) An axis parallel to the z-axis and passing through a corner is 10 3 ml 2 (D) One side is 5 3 ml 2 9. A stepped cylinder (shown in the figure) is having a mass of 50 kg and a radius of gyration k of 0.30 m. The radii R1 and R2 are respectively 0.30 m and 0.60 m. A pull T equal 200 N is exerted on the rope attached to the inner cylinder. The coefficients of static and dynamic friction between cylinder and ground are respectively 0.10 and 0.08 . Which of the following statements are correct? (g = 10 m/s 2 ) O (A) The angular acceleration 2.67rad/s 2 (B) The force kinetic friction is 40 N (C) The acceleration is −3.2 m/s 2 (D) None of the above 10. With reference to fig. of a cube of edge a and mass m, state whether the following are true or false. ( O is the centre of the cube.) (A) The moment of inertia of cube about z-axis is Iz = Ix + Iy (B) The moment of inertia of cube about z ′ is Iz = Iz + ma 2 2 (C) The moment of inertia of cube about z ′′ is = Iz + ma 2 2 (D) Ix = Iy

chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform ω(t) will vary with time t as : (A) (B) (C) (D) 19. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc (A) Continuously decreases (B) Continuously increase (C) First in increases and then decreases (D) Remains unchanged 20. A disc of radius R rolls on a horizontal ground with linear acceleration a and angular acceleration α and angular acceleration α as shown in the figure. The magnitude of acceleration of point P as shown in figure at an instant when its linear velocity is v and angular velocity is ω will be : (A) √(a + rα) 2 + (rω2) 2 (B) ar R (C) √r 2α 2 + r 2ω4 (D) rα 21. The disc of radius r is confined to roll without slipping at A and B. If the plates have the velocities shown then : (A) Angular velocity of the disc of 2 V/r (B) Linear velocity, V0 = V (C) Angular velocity of the disc is 3V/2r (D) None of these 22. A block of mass m is attached to a pulley disc of equal mass m and radius r by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is