Question 4

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:

$$N - mg = ma \implies N = m(g + a)$$

$$a = \frac{g}{2} \implies N = m\left(g + \frac{g}{2}\right) = \frac{3mg}{2}$$

$$s = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}\left(\frac{g}{2}\right)t^2 = \frac{gt^2}{4}$$

$$W_N = N \cdot s \cdot \cos0^\circ = \left(\frac{3mg}{2}\right)\left(\frac{gt^2}{4}\right) = \frac{3mg^2t^2}{8}$$

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