Question

A wooden plank of length $1m$ 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 $0.5m$. The specific gravity of the plank is $0.5$. If the angle $\theta$ by the inclination of that the plank makes with the vertical in the equilibrium position (exclude the case $\theta =0$). Find the value of $\frac{1}{{cos}^2\theta }$

Answer 1

Downward force=Upward force

$mg=\rho Vg=>0.5\times A\times l=1\times \frac{0.5}{\cos \theta }\times A=>\frac{1}{\cos \theta }=l=>\frac{1}{{\cos }^2\theta }=l^2$