Question

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

• A. $0$
• B. $\frac{3m g^2 t^2}{4}$
• C. $ - \frac{m g^2 t^2}{8}$
• D. $ \frac{m g^2 t^2}{8}$

Answer 1

Answer: (B)

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{3 mg }{2}
$
We know that the displacement of a body moving under gravity is given as
$
S = ut +\frac{1}{2} gt ^{2}
$
Here initial velocity is zero.
Now, work done $W =\overrightarrow{ N } \overrightarrow{ S }=\left(\frac{3 mg }{2}\right)\left(\frac{1}{2} gt ^{2}\right)$
$
\Rightarrow W =\frac{3 mg ^{2} t ^{2}}{4}
$