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

Answer

C

Explanation

Let.s consider mass of each rod be m. For equilibrium the torque about point O should be zero.

For rotational equilibrium about point O.
`mg""(a)/(2)sintheta=mg((a)/(2)costheta-asintheta)`
`impliestantheta=(1)/(3)`
`:.theta=tan^(-1)((1)/(3))`