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

Answer 1

Answer: (B)

$> \left( \frac { M } { m } - 1 \right) g$

Answer 2

Equation of motion for M:

Since M is stationary,

T – Mg = 0

⇒ T = Mg …(1)

Since the monkey moves up with an acceleration ‘a’,

T – mg = ma

⇒ T = m(g+a) …(2) Equating (1) and (2), we obtain

Mg = m(g+a)

⇒ a = $\left( \frac { M } { m } - 1 \right) g$

That means, if a > $\left( \frac { M } { m } - 1 \right) g$ , the block M can

be lifted from floor, Hence (2) is the correct choice