Two point masses m each carrying charge `-q and +q` are attached to the ends of a massless rigid non-conducting rod of length l. The arrangement is placed in a uniform electric field E such that the rod makes a small angle `5^(@)` with the field direction. The minimum time needed by the rod to align itself along the field is ..................

Options

A. `t=pisqrt((2ml)/(3qE))`
B. `t=(pi)/(2)sqrt((ml)/(2qE))`
C. `t=sqrt((ml)/(qE))`
D. `t=2pisqrt((ml)/(E))`

Answer

B

Explanation

`tau=qE(lsintheta), tau=qEl theta`
`I=m((l)/(2))^(2)+m((l)/(2))^(2)=(ml^(2))/(2)`
`tau=Ialphaimpliesalpha=(tau)/(I)omega^(2)=(2qE)/(ml)`
`T=(2pi)/(omega)=(2pi)/(sqrt((2qE)/(ml)))=2pisqrt((ml)/(2qE)), t=(T)/(4)=(2pi)/(4)sqrt((ml)/(2qE))=(pi)/(2)sqrt((ml)/(2qE))`