Four solid spheres are made to move on a rough horizontal surface. Sphere `P` is given a spin and released. Sphere `Q` is given a forward linear velocity. Spheres `R` and `S` are given linear and rotational motions as shown in the figure. Directions of the friction force on spheres `P,Q,R,S` are respectively.
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A solid sphere is set into motion on a rough horizontal surface with a linear velocity v in the forward direction and an angular velocity v/R in the anticlockwise direction as shown in the figure. Find the linear speed of the sphere, when it stops rotating.

A solid homogeneous sphere is moving on a rough horizontal surface, partily rolling and partly sliding. During this kind of motion of the sphere.

A solid sphere has combined linear and rotation motion as shown in figure. The velocity of its centre of mass when it starts pure rolling is (R = radius of sphere)

A solid sphere has combined linear and rotation motion as shown in figure. The velocity of its centre of mass when it starts pure rolling is (R = radius of sphere)

A solid sphere has combined linear and rotation motion as shown in figure. The velocity of its centre of mass when it starts pure rolling is (R = radius of sphere)

A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface partly rolling and partly sliding. During this kind of motion of the sphere

A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere.

A solid homogeneous sphere is moving on a rough horizontal surface, partily rolling and partially sliding. During this kind of motion of the sphere.

A solid sphere of radius R is set into motion on a rough horizontal surface with a inear speed v_(0) in forward direction and an angular with a linear speed v_(0) in forward directioin and an angular velocity omega_(0)=v_(0)//2R in counter clockwise direction as shown in figure. If coefficient of friction mu then find a. the time after which sphere starts pure rolling, b. the linear speed of sphere when it starts rolling and c. the work down by friction over a long time.