A sphere moving with a velocity `v_(0)` on a smooth surface suddenly enters on a rough horizontal surface as shown in Fig. State which of the following statements are true or false

a. The sphere loses translational kinetic energy and gains rotational kinetic energy.
b. The total energy of the sphere is conserved.
c. The angular momentum of the sphere about any point `OD` the surface is conserved.
d. The final velocity attained by the centre of mass is `2v_(0)//3`.

Explanation

a. True: The friction force retards the motion of centre of mass and acelerates the rotational motion with respect to centre of mass.
b. False: Energy is not conserved because friction force does negative work.
c.True: The frictional force produces no torque about any point on the horizontal surface.
d. False: Conserving angular momentum about a stationary point on the horizontal surface we get
`mv_(0)R=mvR=(2/5mR^(2))omega`
Using the condition of rolling motion, we get
`v=omegaR`
`mv_(0)R=mvR+2/5mv=7/5mvR`