Question

A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\frac{g}{2}$ upwards as shown in the figure. Work done by the normal reaction on the block in time $t$ is:

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

Answer 1

The correct option is B $\frac{3m{g}^2{t}^2}{8}$


From FBD,
Normal reaction force on the block is:
$\Rightarrow N=m(g+a)=m(g+\frac{g}{2})=\frac{3mg}{2}$

Displacement of the block
$S=0+\frac{1}{2}a{t}^2=\frac{1}{2}\left(\frac{g}{2}\right)t^2(\because u=0)$
Here, $a=\frac{g}{2}\left(given\right)$
$\therefore$ Work done = Force $\times$ Displacement
($\because \text{Force is constant}$)
$\Rightarrow W=\frac{3mg}{2}\times \frac{g{t}^2}{4}=\frac{3m{g}^2{t}^2}{8}$