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A uniform rod of mass M and length L leans against a frictionless wall, with quarter of its length hanging over a corner as shown. Friction at corner is sufficient to keep the rod at rest. Then the ratio of magnitude of normal reaction on rod by wall and the magnitude of normal reaction on rod by corner is

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$\frac{2}{\cos θ}$

$\frac{1}{2 \cos θ}$

$\frac{1}{2 \sin θ}$

$\frac{2}{\sin θ}$

answer is A.

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Detailed Solution

The FBD of rod is Taking moment of force about centre of mass

For equilibrium

$N_{2} \times \frac{L}{4} - N_{1} \sin θ \frac{L}{2} = 0$

$∴ \frac{N_{1}}{N_{2}} = \frac{1}{2 \sin θ}$

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