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

(D) $\frac{3 \mathrm{mg}^{2} \mathrm{t}^{2}}{8}$

(A) $-\frac{\mathrm{mg}^{2} \mathrm{t}^{2}}{8}$

(B) $\frac{m g^{2} t^{2}}{8}$

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Work, Power & Energy

A block of mass

m

is kept on a platform which starts from rest with constant acceleration

g /2

upward, as shown in figure. Work done by normal reaction on block in time

t

is:

Answer: (D)

The platform accelerates the block upward at

g /2

, so Newton's second law on the block reads

N - m g = m \frac{g}{2}

, giving

N = \frac{3 m g}{2}

. In time

t

the block rises through

s = \frac{1}{2} (\frac{g}{2}) t^{2} = \frac{g t ^{2}}{4}

, and since the normal force and the displacement point the same way, the work it does is

W = N s = \frac{3 m g}{2} \cdot \frac{g t ^{2}}{4} = \frac{3 m g ^{2} t ^{2}}{8}

. The normal force does positive work here precisely because the support is accelerating the block upward rather than merely holding it.

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option