Question

Two blocks A and B of masses m and M are placed in a platform as shown in the Figure. The friction coefficient between A and B is µ but there is no friction between B and the platform. The whole arrangement is placed inside an elevator which is coming down with an acceleration a(a < g). What maximum horizontal force F can be applied to A without disturbing the equilibrium of the system?

(A) 2µmg 

(B) 2µm(g – a) 

(C) 2µm(g+a) 

(D) 2µma

Answer 1

Correct option is (B) 2µm(g – a)

For maximum force, F; the friction on ‘M’ will be towards Right.

∴ FBD of m;

F – T – f = 0

N + ma = mg

⇒ F = f + T   … (i)

N = mg – ma   … (ii)

∴ FBD of M;

T – f = 0   … (iii)

N₁ + Ma = Mg   … (iv)

From (i) and (iii);

⇒ F = f + f

⇒ F = 2f ; f = µN = µ(mg – ma)

F = µm (g – a)

⇒ F = 2 µm (g – a).

Answer 2

Correct answer is (B) 2µm(g – a)