Question

The boxes of masses $2\text{kg}$ and $8\text{kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\text{kg}$ to strike the ground starting from rest.
$(\text{Use}g=10{\text{m/s}}^2)$ :

• A. $0.2\text{s}$
• B. $0.34\text{s}$
• C. $0.25\text{s}$
• D. $0.4\text{s}$

Answer 1

The correct option is D $0.4\text{s}$

Let tension in the string attached to $2\text{kg}$ mass be $T,$
Tension in the string attached to $8\text{kg}$ mass is $2T$

Using constraing equations,
If acceleration of $8\text{kg}$ mass is $a$, then acceleration of $2\text{kg}$ mass is $2a$

Free body diagram of masses can be drawn as,


From Newtons second law,

$8g-2T=8a\dots \left(i\right)$

$T-2g=4a\dots \left(ii\right)$

on substitution, we get,

$8g-2(2g+4a)=8a$

$4g=16a$

$a=2.5{\text{ms}}^{-2}$

Now, from $S=ut+\frac{1}{2}a{t}^2$

$0.2=\frac{1}{2}\left(2.5\right)t^2$

$\frac{4}{25}=t^2$

$t=\frac{2}{5}=0.4\text{s}$

Hence, option $\left(\text{D}\right)$ is correct.