First slide

Pressure in a fluid-mechanical properties of fluids

Question

A uniform rod of length b = 90 cm capable of turning about its end which is out of water, rests inclined to the vertical. If its specific gravity is 5/9,the length immersed in water (in cm) is_______

Difficult

Solution

$\begin{array}{l} Taking torque about hinge m g \frac{b}{2} \sin θ = f_{B} (b - \frac{x}{2}) \sin θ \\ (A b) d_{m} g \frac{b}{2} = (A x) d_{L} g (\frac{b x}{2}); \frac{5}{9} \frac{b^{2}}{2} = b x - \frac{x^{2}}{2} \\ By solving it x = \frac{b}{3} = \frac{90}{3} = 30 cm \end{array}$

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