A uniform rod of length b capable of tuning about its end which is out of water, rests inclined to the vertical. If its specific gravity is 5/9, find the length immersed in water.

Options

A. L
B. `(1)/(2)L`
C. `(1)/(4)L`
D. 3L

Answer

A

Explanation

For rotational equilibrium `B(2L-(x)/(2))cos theta = mg.L cos theta`
`rho.A.x(2L-(x)/(2))=0.75rhoA.2L.L`
`2Lx=(x^(2))/(2)=(3)/(2)L^(2)`
`-3L^(2)+4Lx-x^(2)=0`
`x^(2)-4Lx+3L^(2)=0`
`x=L`