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A pulley is mounted on a stand which is placed over a weighing scale. The combined mass of the stand and the pulley is M₀. A light string passes over the smooth pulley and two masses m and M (> m) are connected to its ends (see figure). Find the reading of the scale when the two masses are left free to move

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$\frac{Mmg}{M + m} + M_{0} g$

$\frac{3 Mmg}{M + m} + M_{0} g$

$\frac{4 Mmg}{M + m} + M_{0} g$

$\frac{2 Mmg}{M + m} + M_{0} g$

answer is C.

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Detailed Solution

For motion of the two masses we can write :
$\begin{aligned} Mg - T = {Ma}_{\dots \dots} (1) \\ T - mg = ma \dots . . (2) \end{aligned}$
Solving $T = \frac{2 Mmg}{M + m}$
Now we consider the equilibrium of the stand and pulley system

N = normal force between the stand and the scale = Reading of the scale N = 2T + M_og
$N = \frac{4 Mmg}{M + m} + M_{0} g$

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