Question

In the figure the block of mass M is at rest on the floor. The acceleration with which a monkey of mass m should climb up along the rope of negligible mass so as to lift the block from the floor is,

• A. $=(\frac{M}{m}-1)g$
• B. > $(\frac{M}{m}-1)g$
• C. $=\frac{M}{m}g$
• D. > $\frac{M}{m}g$

Answer 1

The correct option is B > $(\frac{M}{m}-1)g$

Equation of motion for M:
Since M is stationary, T – Mg = 0
$\Rightarrow T=Mg$ …(1)


Since the monkey moves up with an acceleration ‘a’, T – mg = ma
$\Rightarrow T=m(g+a)$ …(2)

Equating (1) and (2), we obtain
$Mg=m(g+a)\Rightarrow a=(\frac{M}{m}-1)g$
That means, if a > $(\frac{M}{m}-1)g$, the block M can be lifted from floor