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 of mass m is placed on a rough incline plane as shown in figure. The coefficient of friction (mu) is insufficient to start pure rolling. The sphere slides length l on incline from rest and its kinetic energy becomes k. Then work done by friction will be

A solid sphere is thrown on a horizontal rough surface with initial velocity of centre of mass V_0 without rolling. Velocity of its centre of mass when its starts pure rolling is

The uniform solid sphere shown in the figure has a spherical hole in it. Find the position of its centre of mass.

A hollow sphere of mass 'm' and radius 'R' are placed on horizontal surface and a horizontal force 'F' starts acting at a distance 'x' from its top most as shown in the figure.The value of 'x' such that hollow sphere starts pure rolling without use of friction is

Three solid sphere of mass M and radius R are placed in contact as shown in figure. Find the potential energy of the system ?

A solid sphere of mass M and radius R is in pure rolling as shown in figure. The angular momentum of the sphere about the origin is (linear velocity of centre of mass is v_0 , in positive x-direction)

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.

A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . They y -coordinate of the centre of mass of the remaining sphere is

A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

A solid sphere is in pure rolling motion on an inclined surface having inclination theta