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A simple pendulum consists of a small sp...

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 placed in a uniform electric field of strength `E` directed vertically upwards. With what period will pendulum oscillate if the electrostatic force acting on the sphere is less than the gravitational force ?

Text Solution

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The two forces acting on the bob are shown in figure

`g_("eff")` in this case will be `(W-F_(e))/(m)`
or `g_("eff")=(mg-qE)/(m)=g-(qE)/(m)`
`therefore T=2pisqrt( (l)/(g_("eff")))=2pisqrt((l)/(g-(qE)/(m)))`
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