A simple pendulum having length l and mass 'm' is suspended between two plates having uniform electric field 'E' as shown in figure. The bob is given a charge q . The time period &

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A simple pendulum having length l and mass 'm' is suspended between two plates having uniform electric field 'E' as shown in figure. The bob is given a charge q . The time period 'T' of its vibration is

TestHub · Accepted Answer

The forces acting on the bob of the pendulum are the gravitational force $m g$ acting downwards and the electrostatic force $qE$ acting downwards (since the electric field $E$ is directed downwards and the charge $q$ is assumed positive).

The net downward force on the bob is $F_{n e t} = m g + qE$ .

The effective acceleration due to gravity is $g_{e ff} = \frac{F _{n e t}}{m} = g + \frac{qE}{m}$ .

The time period of a simple pendulum is given by $T = 2 π \frac{l}{g _{e ff}}$ .

Substituting the value of $g_{e ff}$ , we get $T = 2 π \frac{l}{g + \frac{qE}{m}}$ .

Answer: $2 π \frac{l}{g + \frac{Eq}{m}}$

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