A small sphere carrying a charge is hanging in between two parallel plates
by a string of length . Time period of pendulum is . When parallel plates are
charged, the time period changes to The ratio is equal to

The correct answer is:

The motion of sphere is simple harmonic. It’s time period () is given by

…(i)
where is length of string, g the acceleration due to gravity.
When sphere is placed in electric field. () force due to electric field acts on the sphere-1

where is charge on sphere.
Hence, resultant acceleration is

…(ii)
Dividing Eq. (ii) by Eq. (i), we get