Question

A block of mass $m$ is kept on a platform which starts from rest with a constant acceleration $g/2$ upwards, as shown in the figure. Work done by normal reaction on block in time $t$ is___?

• A. $0$
• B. $\frac{3m{g}^2{t}^2}{8}$
• C. $-\frac{m{g}^2{t}^2}{8}$
• D. $\frac{m{g}^2{t}^2}{8}$

Answer 1

Answer: (B)

$\frac{3m{g}^2{t}^2}{8}$

Since the acceleration is in upward direction, there will be a pseudo force acting on the block given as:

$F_p=m\times \frac{g}{2}$

Now applying the force balance on the block

$N-mg=\frac{mg}{2}$

$\Rightarrow N=\frac{3mg}{2}$

We know that the displacement of a body moving under gravity is given as

$S=ut+\frac{1}{2}g{t}^2$

Here initial velocity is zero.

Now, work done $W=\overrightarrow{N}\overrightarrow{S}=\left(\frac{3mg}{2}\right)\left(\frac{1}{2}g{t}^2\right)$

$\Rightarrow W=\frac{3m{g}^2{t}^2}{4}$.