Consider a parallel plate capacitor having an electric field `E` inside it as shown in the adjacent figure. A particle of mass `m` and charge `q` is hanging inside the capacitor through a light inextensible string of length. The time period of this pendulum of small oscillations is

Options

A. `T= 2pisqrt((l)/(g+(qE//m)))`
B. `T= 2pisqrt((l)/(sqrt(g^(2)+(q^(2)E^(2))/(m^(2))-(2qgE)/(m))))`
C. `T= 2pisqrt((l)/(sqrt(g^(2)+(q^(2)E^(2))/(m^(2))+(2qgE)/(m))))`
D. none of these

Answer

d

Explanation

Apart from tension `T`, two constant force `qE` and `mg` are acting.

Resultant of these is
`F=sqrt((qE)^(2)+(mg)^(2)+2mgE cos theta)`
`g_(eff)=(F)/(m)`
`T= 2pi sqrt((l)/(g_(eff)))= 2pisqrt((l)/((F//m)))`