On a smooth horizontal beam of radius 1 m, we have placed two identical boards, connected by a hinge, as shown in Figure. Boards are in equilibrium, and the angle between the boards is 90°. Find the length of each board ℓ (in m).

Engineering

Physics

Conservation of Angular Momentum

Question

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About hinge, τ = 0

$\Rightarrow mg \frac{ℓ}{2} \sin 45^{\circ} = N \times 1 \tan 45^{\circ}$

$N = \frac{mgℓ}{2 \sqrt{2}}$

2N cos 45° = 2 mg

$\Rightarrow N = mg \sqrt{2} = \frac{mgℓ}{2 \sqrt{2}}$

⇒ ℓ = 4 m

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