Rotational MotionHard

Question

A plank with a uniform sphere placed on it, rests on a smooth horizontal plane. Plank is pulled to right by a constant force F. If the sphere does not slip over the plank
                                            

Options

A.Acceleration of centre of sphere is less than that of the plank
B.Acceleration of centre of sphere is greater than the plank because friction acts rightward on the sphere
C.Acceleration of the centre of sphere may be towards left
D.Acceleration of the centre of sphere relative to plank may be greater than that of the plank relative to floor

Solution

Force diagram of plank and sphereForce diagram of plank and sphere

f = m2ac ⇒ f × r = m2r2α also ap = a
rα + ac = a ∴ ac = a

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