Block a of mass 4 kg is to be kept at rest against a smooth vertical wall by applying a force F as shown in figure. The force required is :- `(g=10m//s^(2))`

Options

A. Net acceleration of sphere is in the direction of applied force F
B. Net acceleration of point of contact of sphere with plank is equal to acceleration of plank
C. Work done by friction on plank is equal to its linear kinetic energy.
D. Total kinetic energy acquired by the system is equal to work done by force F.

Answer

A, B, D

Explanation

When plank tries to move in the direction of applied force then sphere applies friction on it opposite to this direction. Opposite pair of friction acts on the sphere which is in the direction of applied force. Since no other horizontal force acts on the sphere hence its net acceleration is in the direction of applied force. Sphere performs pure rolling on the plank hence there should not be any relative motion between point of contact of sphere and plank hence both must have same acceleration. Work done by friction on the sphere is equal to its total kinetic energy which is linear and rotational Hence work done by friction is not just equal to linear kinetic energy Total work done by the friction is zero because there is no relative motion between bottom point of sphere and the plank. So total kinetic energy acquired by the system is equal to work done by force F. Force of friction transfers some part of energy from plank to sphere. But there is no loss of energy due to friction. So we can understand that options (a), (b) and (d) are correct