Question

A plank with a uniform sphere placed on it resting on a smooth horizontal plane. Plank is pulled to right by a constant force $F$. If sphere does not slip over the plank. Which of the following is incorrect?

• A. acceleration of the centre of sphere is less than that of the plank
• B. work done by friction acting on the sphere is equal to its total kinetic energy
• C. total kinetic energy of the system is equal to work done by the force $F$
• D. none of these

Answer 1

Answer: (D)

none of these

Let the acceleration of COM of sphere be $a_s$ and that of plank be $a_p$.

Friction force acts on the sphere in forward direction and equal friction force will act on plank backwards.

As point A doesnot slide over plank, so $a_A=a_p$

$a_s+R\alpha =a_p⟹a_s<a_p$

Work-energy theorem: $W_{allforces}=\Delta K.E$

For sphere: net external force is $f$ only

Thus $W_f=\Delta K.E$ (of sphere)

As the sphere was at rest initially, $⟹W_f=K.E$ (of sphere)

For sphere + plank system:

Friction will be an internal force and workdone by internal forces cancels out each other.

Thus $W_F=\Delta K.E$ (of system)

As the system was at rest initially, $⟹W_F=K.E$ of the system