A simple pendulum consists of a small sphere | vedclass

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Question

(C) The forces acting on the sphere are the gravitational force $mg$ (downwards) and the electric force $qE$ (upwards, since the field is vertically u

Vedclass · Accepted Answer

$2 \pi \sqrt{\frac{l}{g-\frac{q E}{m}}}$

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(C) The forces acting on the sphere are the gravitational force $mg$ (downwards) and the electric force $qE$ (upwards, since the field is vertically upwards and charge is positive).The net downward force $F$ is given by $F = mg - qE$.We can write this as $F = m(g - \frac{qE}{m})$.Thus, the effective acceleration due to gravity $g'$ is $g' = g - \frac{qE}{m}$.The time period $T$ of a simple pendulum is given by $T = 2\pi \sqrt{\frac{l}{g'}}$.Substituting the value of $g'$, we get $T = 2\pi \sqrt{\frac{l}{g - \frac{qE}{m}}}$.

$A$ simple pendulum consists of a small sphere of mass $m$ suspended by a thread of length $l$. The sphere carries a positive charge $q$. The pendulum is allowed to do small oscillations in a uniform electric field $E$ with direction vertically upwards. The time period of oscillation is

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