In Fig. 5.1, the co-efficient of friction between the floor and the body B is 0.1. The co-efficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B.The mass of A is m/2 and of B is m. Which of the following statements are true?

(a) The bodies will move together if F = 0.25 mg.

(b) The body A will slip with respect to B if F = 0.5 mg.

(c) The bodies will move together if F = 0.5 mg.

(d) The bodies will be at rest if F = 0.1 mg.

(e) The maximum value of F for which the two bodies will move together is 0.45 mg.