Question

The friction coefficient between the two blocks shown in figure is $\mu$ but the floor is smooth. Assume the entire system is kept inside an elevator coming down with an acceleration a < g.

• A. 2m(g-a),
• B. 2m(g-a),
• C. 2,
• D. None of these

Answer 1

The correct option is A

2m(g-a),

As it is at rest with respect to the elevator

$\sum F_x=0$ Block M,MN=T

$\sum F_y=0$ $\Rightarrow T=\mu m(g-a)$ .........(2)

N+ ma = Mg

$\Rightarrow$N=m(g-a) .........(1)

F=T+$\mu$N
=T+ $\mu$m(g-a) ..........(3)

From (2) and (3)

F= 2$\mu$m (g - a)

Case(B)

When F=4$\mu$m(g-a) For block M
For block m, $\sum F_x=M{a}_1$
$\sum F_x=m{a}_1$

The magnitude of acceleration will be the same as they are constrained by the string.

$\therefore F-T-\mu M(g-a)=M{a}_1$ (For block m)

T - $\mu m(g-a)=M{a}_1$ (For block M)

=F - 2$\mu m(g-a)=(M+m)a_1$

$\Rightarrow 4\mu m(g-a)-2\mu m(g-a)=(M+m)a_1\Rightarrow a_1=\frac{2\mu m(g-a)}{M+m}$