Question

The system shown is figure is released from rest. String is massless and pulley is smooth. Find the work done by string on 1 kg block in the time interval of $2s$. (Take $g=10m/s^2$)

• A. $48J$
• B. $96J$
• C. $144J$
• D. $192J$

Answer 1

The correct option is D $192J$

Acceleration of each block=$a=\frac{m_2-m_1}{m_2+m_1}g$

$=\frac{4-1}{4+1}g=\frac{3}{5}g$

Thus the distance covered by block in 2s, S =$\frac{1}{2}a{t}^2=\frac{1}{2}\times \frac{3}{5}g\times 2^2=12m$

Considering forces acting on $1kg$ block,

$m_{1}a=T-m_{1}g$

$⟹T=\frac{8}{5}g$

Thus work done by tension in the interval=$TS$

$=\frac{8}{5}g\times 12$

$=192J$