CENTRE OF MASS OF SOLID HEMI-SPHERE

CENTRE OF MASS OF UNIFORM HEMI-SPHERICAL SHELL

A solid sphere of radius R is rolled by a force F acting at the topo of the sphere as shown in the figure. There is no slipping and initially sphere is in the rest position, then (CM= centre of mass)

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 uniform solid sphere of radius R has a hole of radius R//2 drilled inside it. One end of the hole is at the centre of the sphere while the other is at the boundary. Locate centre of mass of the remaining sphere..

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 ?

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 ?