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A small mass attached to a string rotates on a frictionless tabletop as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will:-
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Important Questions on Rotational Mechanics

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ABC is an equilateral triangle with O as its centre. F1, F2 and F3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of F3 is:-
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When a mass is rotating in a plane about a fixed point, its angular momentum is directed along,
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If a solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m/s. It collides with a horizontal spring of force constant 200 N/m. The maximum compression produced in the spring will be
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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
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A circular platform is mounted on a frictionless vertical axle. Its radius R=2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s-1 relative to the ground. Time taken by the man to complete one revolution is
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A solid cylinder of mass50 kg  and radius 0.5 m is free to rotate about a horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 rev/s2 is 
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The ratio of the accelerations for a solid sphere (mass M and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is
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A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown.
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The tension in the string is increased gradually and finally m moves in a circle of radius R02. The final value of the kinetic energy is:-