# A uniform cylinder of mass rests on two rough horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force a) Since horizontal acceleration is provided by the friction acting on the cylinder, its translation kinetic energy is equal to work done by this friction b) Since moment about instantaneous axis of rotation is produced by force kinetic is equal to work done by where ismoment of inertia about the instantaneous axis of rotation and is the angular velocity c) Since cylinder is moving, energy is lost against friction d) Work done by + work done by friction on cylinder =total KE of the cylinder

## Question ID - 100837 :- A uniform cylinder of mass rests on two rough horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force a) Since horizontal acceleration is provided by the friction acting on the cylinder, its translation kinetic energy is equal to work done by this friction b) Since moment about instantaneous axis of rotation is produced by force kinetic is equal to work done by where ismoment of inertia about the instantaneous axis of rotation and is the angular velocity c) Since cylinder is moving, energy is lost against friction d) Work done by + work done by friction on cylinder =total KE of the cylinder

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 (b,a) When force acts vertically downwards on the thread, the thread unwinds and the cylinder rotates clockwise. Hence, its surface tries to slip over the planks in a backward direction.Hence, a friction comes into existence and acts on the cylinder in a forward direction (rightward direction). It is the only horizontal force acting on the cylinder. Due to the friction, cylinder experiences a rightward translational acceleration.But the point at which the friction acts  remains always at rest, therefore no energy is lost against the friction Since the work is done by and no energy is lost against the friction, therefore total kinetic energy of the cylinder at any instant is equal to work done by . Hence, options (a) and (c) are incorrect and option (d) is correct If is the moment of inertia of a body about its instantaneous axis of rotation, then the total KE of the rotating body is equal to . Hence, option (b) is correct

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