A man (mass = m) is standing on a platform (mass = M). By pulling the string he causes the motion of platform. What is the ratio of $\frac{M}{m}$ such that the man and the platform move together?

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answer is 7.

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Detailed Solution

Let tension in string in hands of man is $\frac{T}{4}$ .

$\begin{array}{l} \frac{T}{4} = m g \\ T = 4 m g \end{array}$

Now, move platform slowly.
So a = 0
$T + \frac{T}{2} + \frac{T}{4} + \frac{T}{4} = (M + m) g \frac{8 T}{4} = (M + m) g \frac{8}{4} \times 4 m g = (M + m) g 8 m = M + m \begin{array}{l} 7 m = M \\ 7 = \frac{M}{m} \end{array}$

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