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Moment of inertia of body resists a change in its state of angular momentum and depends on the mass of the body, size and shape of the body, distribution of mass about the axis of rotation, position and orientation of the axis of rotation. Three bodies, a ring, a solid sphere, a solid cylinder roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical.
For increasing the angular velocity of an object by 10%, the kinetic energy has to be increased by
(a) A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping. (b) Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.
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