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What is the frictional force on a drum of radius R and mass M if it rolls down without slipping along an inclined plane of angle θ?

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Important Questions on Rotational Mechanics

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KCET (UG)
IMPORTANT
A hollow sphere of mass M and radius R is rotating with angular frequency ω. It suddenly stops rotating and 75% of kinetic energy is converted to heat. If S is the specific heat of the material in J kg K-1 then rise in temperature of the sphere is (M.I. of hollow sphere =23 MR2)
EASY
KCET (UG)
IMPORTANT
Three objects, A:(a solid sphere), B:(a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work W required to bring them to rest, would satisfy the relation
MEDIUM
KCET (UG)
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A uniform circular disc of radius r placed on a rough horizontal plane has initial velocity v0 and angular velocity ω0 as shown. The disc comes to rest after moving some distance in the direction of motion. Then

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EASY
KCET (UG)
IMPORTANT
A solid sphere is rolling on a frictionless surface as shown in the figure with a translational velocity v m s-1. If it is to climb the inclined surface, then v should be
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MEDIUM
KCET (UG)
IMPORTANT
The speed of a homogeneous solid sphere after rolling down on an inclined plane of vertical height h from rest without sliding is
EASY
KCET (UG)
IMPORTANT

A sphere S rolls without slipping, moving with a constant speed on a plank P. The friction between the upper surface of P and the sphere is sufficient to prevent slipping, while the lower surface of P is smooth and rests on the ground. Initially, P is fixed to the ground by a pin N. If N is suddenly removed, 

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KCET (UG)
IMPORTANT
Four identical uniform rods of mass m = 6 kg each are welded their ends to form a square and then welded to a uniform ring having mass m = 4 kg and radius R = 1 m. The system is allowed to roll down a rough incline of inclination θ = 3 0 . ( where g is in m s-2)

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The force of friction between the system and the plane is
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KCET (UG)
IMPORTANT
A cylinder of mass m is kept on an inclined plane having an angle of inclination 30°. Axis of the cylinder makes an angle 30° with the line along the greatest slope. Assuming that cylinder rolls without slipping, the acceleration of the cylinder is

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