Question

A simple pendulum has a length l, mass of Bob m. the Bob is given a charge q Coulomb. the pendulum is suspended between the vertical plates of charged parallel plate capacitor. which produces a uniform electric field of strength E between there plates, then assuming that it does not collide with the plate calculate the time period T =

Answer 1

you should remember that time period of simple pendulum is given by, $T=2\pi\sqrt{\frac{l}{a_{eff}}}$

where, $\bf{a_{eff}}$ means effective acceleration or net acceleration acting on bob and l is length of pendulum.

due to electric field, acceleration of bob , $a_E=\frac{qE}{m}$ along positive direction of x - axis.

and acceleration of bob due to gravity, $a_g=g$ vertically downward direction.

now in vector form, effective acceleration will be, $a_{eff}=\frac{qE}{m}\hat{i}-g\hat{j}$

hence, magnitude of $a_{eff}=\sqrt{\left(\frac{qE}{m}\right)^2+g^2}$

now time period will be $\bf{T=2\pi\sqrt{\frac{l}{\left(\frac{qE}{m}\right)^2+g^2}}}$

Answer 2

Answer:

this is the required answer hope it helps❤