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When a body is rolling without slipping on a rough horizontal surface, the work done by 'friction is

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Important Questions on System of Particles and Rotational Motion

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A solid spherical ball is rolling without slipping down an inclined plane. The fraction of its total energy associated with rotation is
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A solid cylinder of mass M and radius R rolls down the inclined plane from height h without slipping. The speed of its centre of mass when it reaches the bottom is:
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An inclined -plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to
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An object slides down a smooth incline and reaches the bottom with velocity v. If same mass is in the form of a ring and it rolls down an inclined plane of same height and angle of inclination, then its velocity at the bottom of inclined plane will be
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A swimmer while jumping into river from a height easily forms a loop in air if
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A child sitting at the centre of a rotating stool has his arms stretched. If he folds his arms, his angular speed about the axis of rotation, 
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The position vector of three particles of masses, m1=1 kg, m2=2 kg and m3=4 kg are r1=(i^+j^) m, r2=(2i^+5j^) m and r3=(2i^-j^) m respectively. The position vector of their center of mass is,