Question

In the shown pulley-block system, strings are light. Pulleys are massless and smooth and system is released from rest. In $0.6$ second, what is the work done by gravity on $20\text{kg}$ and $10\text{kg}$ block respectively ?
Take $[g=10{\text{m/s}}^2]$

• A. $120\text{J};30\text{J}$
• B. $30\text{J};120\text{J}$
• C. $240\text{J};-60\text{J}$
• D. $-240\text{J};60\text{J}$

Answer 1

The correct option is C $240\text{J};-60\text{J}$

Using constraints, if acceleration of $10\text{kg}$ is $a$ upwards, acceleration of $20\text{kg}$ is $2a$ downwards,

FBD for both bodies

$2T-10g=10a.....\left(1\right)20g-T=40a.......\left(2\right)$

From (1) & (2)

$30g=90a$
$a=\frac{g}{3}$

Displacement of $20\text{kg}$ block

$=\frac{1}{2}a{t}^2=\frac{1}{2}\times \frac{2g}{3}\times {0.6}^2=1.2\text{m}$

Therefore as per the pulley system arrangement
Displacement of $10\text{kg}=\frac{1.2}{2}=0.6\text{m}$

$\therefore$ Work done on $20\text{kg}$ block by gravity
$=mgh=20\times 10\times 1.2=240\text{J}$

Work done on $10\text{kg}$ block
$=-mg\frac{h}{2}$ (moving up)
$=-10\times 10\times \frac{1.2}{2}$
$=-60\text{J}$

Hence option C is the correct answer