Question

In the figure shown, $6kg$ body is at a distance of $16m$ from the support at $t=0$. The string is cut at $t=1s$ after the system is released from rest. Find the time $\left(\text{in sec}\right)$ after which the $6kg$ block will hit the support. Take $g=10\frac{m}{s^2}.$

Answer 1

The FBDs of the blocks are as shown


As we know, the acceleration of the system is given by
$a=\frac{\text{(Supporting Force-Opposing Force)}}{\text{Total mass}}$
$\Rightarrow a=\frac{4g}{4+6}=4m/s^2$

As string is cut at $t=1s$, velocity after $1s$ is
$v=u+at=0+4\times 1=4m/s$
Distance travelled during this time is
$S=ut+\frac{1}{2}\times a{t}^2=0+\frac{1}{2}\times 4\times 1^2=2m$

Hence, after string is cut, it has to travel a distance of $(16-2)=14m$ with a velocity of $4m/s$
Therefore, time taken by block to strike the support is
$t=\frac{14}{4}=3.5s$