Question

A block of mass $m$ is placed on the floor of lift which is moving with velocity $v=4t^2$, where $t$ is time in second and velocity in $\text{m/s}$. Find the time at which normal force on the block is three times of its weight.

• A. $\left(\frac{3g}{8}\right)s$
• B. $gs$
• C. $\frac{g}{4}s$
• D. $3gs$

Answer 1

The correct option is C $\frac{g}{4}s$

Given velocity $v=4t^2$
$\Rightarrow$ acceleration $a=\frac{dv}{dt}=8t$
Now as lift is moving up
$N=m(g+a)$
$N=m(g+8t)$
Given $N=3mg$
$\Rightarrow 3mg=mg+3mt$
$=2\text{/}mg=8\text{/}mt$
$\Rightarrow t=\frac{g}{4}s$