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One end of a board of length l is hinged...

One end of a board of length l is hinged on top of a stone protruding from water . Length a of the board is above the point of support (Fig) . What part of the board is below the surface of the water in equilibrium state , if the density of wood is `gamma` ?

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To solve the problem, we need to analyze the forces acting on the board and apply the principles of equilibrium. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Setup We have a board of length \( L \) that is hinged at one end on a stone above the water surface. The length \( a \) of the board is above the point of support, and we need to find the length \( x \) of the board that is submerged in water when the system is in equilibrium. ### Step 2: Identify Forces Acting on the Board 1. **Weight of the Board (W)**: The weight acts downwards at the center of mass of the board, which is at a distance \( \frac{L}{2} \) from the hinge. The weight can be expressed as: \[ ...
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