A horizontal force `P` applied at a height `h` above the centre of a solid cylinder of mass `M`, radius `R`. Determine force of friction in terms of `h` show that friction force is zero for `h=R//2`. Assume that the cylinder rolls without slipping.

A horizontal force F is applied at a height h above the center of a solid cylinder of mass m and radius R . Determine friction, if cylinder rolls without slipping. For what value of h , friction is zero.

A bullet of mass m moving with a velocity of u just grazes the top of a solid cylinder of mass M and radius R resting on a rough horizontal surface as shown and is embedded in the cylinder after impact. Assuming that the cylinder rolls without slipping, find the angular velocity of the cylinder and the final velocity of the bullet.

A heavy homogeneous cyliner has mass m and radius R . It is accelerated by a force F which is applied through a rope wound around a light drum of radius r attached to the cylinder (figure) the coefficient of static friction is sufficient for the cylinder to roll without slipping.

A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its centre when it reaches the bottom is.

A solid cylinder of mass 8 kg and radius 50 cm is rolling down a plane inclined at an angle of 30^@ with the horizontal. force of friction on the cylinder is?

A force F is applied horizontally on a cylinder in the line of centre as shown in the figure. The cylinder is on a rough surface of coefficient of fricition mu . The direction of the friction force acting on the cylinder will be