A small sphere carrying a charge `q` is hanging in between two parallel plates by a string of length `L`. Time period of pendulum is `T_(0)`. When parallel plates are charged, the time period changes to `T`. The ratio `T//T_(0)` is equal to

Options

A. `((g+(qE)/m)/g)^(1//2)`
B. `(g/(g+(qE)/m))^(3//2)`
C. `(g/(g+(qE)/m))^(1//2)`
D. None of these

Answer

C

Explanation

`T_0=2pisqrt(l//g)`
When `l rarr` constant then `T prop 1/sqrt(g.)`
`F_("net") implies mg. = mg +qE`
`implies g.= (g+(qE)/(m))`
`T=2pisqrt(l//g.)=2pisqrt(l/((g+(qE)/m))) `
Now `T/T_0=[(g)/(g+(qE)/m)]^(1//2)`