CENTRE OF MASS OF SOLID HEMI-SPHERE

CENTRE OF MASS OF UNIFORM HEMI-SPHERICAL SHELL

A solid sphere of radius r and mass m rotates about an axis passing through its centre with angular velocity omega . Its K.E . Is

A uniform sphere has radius R . A sphere of diameter R is cut from its edge as shown. Then the distance of centre of mass of remaining portion from the centre of mass of the original sphere is

A small mass m is transferred from the centre of a hollow sphere of mass M to infinity. Find work done in the process. Compare this with the situation if instead of a hollow sphere, a solid sphere of same mass were there.

A spherical cavity is formed a solid sphere by removing mass from it. The resultant configuration is shown in figure. Find out the moment of inertia this configuration about the axis through centre of the solid sphere as shown . Take mass M( uniform ) for the configuration and radius R for solid sphere and radius R//2 for cavity.

A solid sphere of mass M and radius R is hit by a cue at a height h above the centre C. for what value of h the sphere will rool without slipping ?