Question

A block of mass \(m\) is kept on a platform which starts from rest with constant acceleration \(\dfrac{g}{2}\) upward, as shown in fig. work done by normal reaction on block in time \(t\) is:

m \( { }_{\text {motum }} \hat{q}_{ a }=\frac{ g }{2} \)

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

Answer 1

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

Given:
Block mass $=m$
Initial velocity $U=0$
Acceleration $a=\frac{g}{2}\text{Upwards}$


Normal reaction on block,
$N-mg=ma\Rightarrow N=mg+\frac{mg}{2}$
$\Rightarrow N=\frac{3mg}{2}$

Now, work done by normal reaction ${}^{\prime }{N}^{\prime }$ on block in time $t,$

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

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

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