There is an insulator rod of length L and of negligible mass with two small balls of mass m and electric charge Q attached to its ends. The rod can rotate in the horizontal plane around a vertical axis crossing it at a `L//4` distance from one of its ends.
What is the time period of the SHM as mentioned in previous question?

Options

A. `2pisqrt((mL)/(QE))`
B. `2pisqrt((2mL)/(3QE))`
C. `2pisqrt((5mL)/(QE))`
D. `2pisqrt((5mL)/(4QE))`

Answer

D

Explanation

For small angular displacement `theta` from equilibrium position restoring torque `=QE sin theta((3L)/4-L/4)=lalpha`
`(sincetheta is very small sin theta approx theta)`
`Rightarrow alpha=((QEL)/21)(-theta)Rightarrow omega=sqrt(((QEL)/21))` where I (moment of inertia)`=((mL^(2))/16+(9mL^(2))/16)`
Time period `(T)=2pi//omega=2pisqrt((5mL)/(4QE)`