A disc of mass M and radius R is rolling without slipping down ay inclined plane. Show that the acceleration of the centre of mass of the disc is `2/3 g sin theta`. Given, angle of inclination of the plane is `theta` and moment of inertia .of the disc is `(MR^2)/2`

A uniform solid sphere of mass M and radius R rolls down an inclined plane making an angle theta with the horizontal without slipping. Show that the acceleration of the sphere is (5)/(7)gsin theta . [ Given: moment of inertia of the sphere is (2)/(5) MR^(2) ]

A circular disc rolls down on an inclined plane without slipping. What fraction of its total energy is translation ?

A particle is sliding down along an inclined plane. Frictional force is 0.2 times the normal reaction , and the inclination of the plane is 60^@ . What is the acceleration of the particle ? If the mass of the particle is 1g , find the change in the sum of potential and kinetic energies of the particle as it slides down the plane by 1 m.

A circular disc of mass m and radius r is rolling over a horizontal table top with angular velocity omega . Prove that the total energy of the disc , K = (3)/(4) m omega ^(2) r^(2) .

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?