An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB=BD, and the angle made by AB with downward vertical is `theta`, then :

Options

A. `tan theta = 2/sqrt(3)`
B. `tan theta =1/(2sqrt(3))`
C. `tan theta = 1/3`
D. `tan theta =1/2`

Answer

C

Explanation

For equilibrium of L-shaped object the line of action of Tension is along a vertical line passing through its centre of mass (Com). Suppose total mass is 2M.

In `trianglePQC`
`tan theta =(L//4)/(3L/4) = 1/3 rArr` i.e., option (C)