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Question

A wooden plank of length 1 m and uniform cross section is hinged at one end to the bottom of a tank as shown in the figure. The tank is filled with water up to a height of 0.5 m. The specific gravity of the plank is 0.5. If the angle θ by the inclination of that the plank makes with the vertical in the equilibrium position (exclude the case θ=0). Find the value of 1cos2θ

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Solution

Downward force=Upward force
mg=ρVg=>0.5×A×l=1×0.5cosθ×A=>1cosθ=l=>1cos2θ=l2

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