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A solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of static friction in upward and downward motion respectively is

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Important Questions on System of Particles and Rotational Motion

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Two solid spheres of different mass, radii and density roll down a rough inclined plane under identical situation. Their time to come down is independent of their
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A thin circular ring first slips down a smooth incline then rolls down a rough incline of identical geometry from same height. Ratio of time taken in the two motion is
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The thin rod shown below has mass M and length L. A force F acts at one end as shown and the rod is free to rotate about the other end in the plane of force. Initial angular acceleration of the rod is

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Angular momentum L of a particle of linear momentum p at a position r relative to the origin O, about it is given by L=rp_____θ .
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Rotational _____ energy of a rigid body of moment of inertia I rotating with angular velocity ω about a fixed axis is 12Iω2.
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Moment of inertia of a hollow cylinder of mass M and radius R about the axis of cylinder is _____R2.
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A body rolls down on an inclined plane. If its kinetic energy of rotational motion is 40% of its kinetic energy of translational motion, then the body is
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 a×(b+c)=a×b_____a×c.