A metal ball suspended from a long thread is held between the plates of a capacitor , as shown in Fig, How will the oscillations of this pendulum change, if the ball and the plates of two capacitor are charged ?

Answer

Time period of ball will decrease

Explanation

Suppose charge given to the ball is `+q`. Let plate A of capacitance be given positive charge and plate B be given an equal negative charge, so as to produce a horizontal electric field E.
The equilibrium position of the ball will change from O to A making angle `theta` with vertical.
The ball experiences two forces : qE along horizontal and mg along vertical such that
`tan theta = (qE)/(mg)`
The resultant force on the ball
`F' = mg' = sqrt((mg)^(2) + (qE)^(2))`
`g' = sqrt(g^(2) + (qE//m)^(2))`
`:.` Time period of vibration of ball
`t' = 2pi sqrt((l)/(g')) = 2pi [(l)/(sqrt(g^(2) + (qE//m)^(2)))]^(1//2)`
As `g' gt g`, therefore `t' lt t`
i.e., time period of vibration of the ball will decrease.