Question

Two blocks of mass $10\text{kg}$ and $2\text{kg}$ respectively are connected by an ideal string passing over a fixed smooth pulley as shown in figure. A monkey of mass $8\text{kg}$ starts climbing the string with a constant acceleration of $2{\text{ms}}^{-2}$ with respect to the string at $t=0$. Initially, the monkey is $2.4\text{m}$ from the pulley. Find the time taken by the monkey to reach the pulley.

• A. $8\text{sec}$
• B. $6\text{sec}$
• C. $4\text{sec}$
• D. $2\text{sec}$

Answer 1

The correct option is D $2\text{sec}$

Given,
mass of the monkey, $m_m=8\text{kg}$
and its acceleration w.r.t the rope, $a_0=2{\text{m s}}^{-2}$

If the acceleration of rope is $a$ downward, acceleration of monkey w.r.t ground, $a_m=a_0-a$


From free body diagram of monkey:

$T-8g-T_1=8\times a_m=8(2-a)....\left(1\right)$

From free body diagram of block of mass $2\text{kg}$:

$2g-T_1=2a.........\left(2\right)$

From free body diagram of block of mass $10\text{kg}$:

$T-10g=10a.........\left(3\right)$

From $\left(1\right)$, $\left(2\right)$ and $\left(3\right)$, we have

$(10a+10g)-8g-(2g-2a)=16-8a$

$\Rightarrow a=\frac{4}{5}$

Now, net acceleration of monkey,
$a_m=a_0-a=2-\frac{4}{5}$

$\Rightarrow a_m=1.2{\text{ms}}^{-2}$

Using equation of motion, time taken by the monkey to reach the pulley,

$t=\sqrt{\frac{2\times S}{a_m}}=\sqrt{\frac{2\times 2.4}{1.2}}=2\text{sec}$

Hence, the correct option is (d).