Question

Block A of mass $m/2$ is connected to one end of light rope which passes over a pulley as shown in the figure. Man of mass $m$ climbs the other end of rope with a relative acceleration of $g/6$ with respect to rope. Find acceleration of block A and tension in the rope.

• A. $\frac{4g}{9},\frac{18mg}{13}$
• B. $\frac{9g}{4},\frac{13mg}{18}$
• C. $\frac{4g}{9},\frac{13mg}{18}$
• D. $\frac{9g}{4},\frac{18mg}{13}$

Answer 1

Answer: (C)

$\frac{4g}{9},\frac{13mg}{18}$

Let acceleration of man with respect to ground is $a_0$ and acceleration of block is $a$.

here, $a+a_0=g/6$ or $a_0=g/6-a$

From FBD of man, $m{a}_0=T-mg$ or $m(g/6-a)=T-mg$

or $T+ma=7mg/6...\left(1\right)$

From FBD of block A: $\frac{m}{2}a=T-\frac{m}{2}g$ or $T-ma/2=mg/2..\left(2\right)$

$\left(1\right)-\left(2\right)\Rightarrow 3ma/2=2mg/3$ or $a=\frac{4g}{9}$

from (2), $T=mg/2+\left(m/2\right)\left(4g/9\right)=\frac{13mg}{18}$