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Applying NLM along 3 Axis

Two uniform r...

Question

Two uniform rods of equal length but different masses are rigidly joined to form an L-shaped body, which is then pivoted about O as shown in the figure. If the system is in equilibrium in the shown configuration. Then the ratio M/m will be:

A

2

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B

3

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C

\sqrt{2}

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D

\sqrt{3}

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Solution

The correct option is D $\sqrt{3}$
Taking Moments about point 'O'
clockwise moments = Anticlockwise moments,
$M g \times \frac{l}{2} s i n (30^{o})$ = $m g \times \frac{l}{2} s i n (60^{o})$ ,

$\Rightarrow \frac{M}{2} = m \frac{\sqrt{3}}{2}$

$∴ \frac{M}{m} = \sqrt{3}$

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