A block of mass m is kept on a platform which starts from rest with a constant acceleration g / 2 upwards,…

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

1. $-\frac{m{g}^2{t}^2}{8}$
2. $\frac{m g^2{t}^2}{8}$
3. $0$
4. $\frac{3 m g^2{t}^2}{8}$

Solution

$N-mg=\frac{mg}{2}$
$N=\frac{3mg}{2}$
$s=ut+\frac{1}{2}a{t}^2$
$=0+\frac{1}{2}\frac{g}{2}{t}^2$
$=\frac{g}{4}$$t^2$
$W_N=\frac{3mg}{2}\times \frac{g}{4} t^2$
$=\frac{3m{g}^2{t}^2}{8}=\frac{3m{g}^2{t}^2}{8}$

Asked in: JEE Main 2019 (10 Jan Shift 1)

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