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The bob of a pendulum of mass 'm' suspen...

The bob of a pendulum of mass 'm' suspended by an inextensible string of length L as shown in the figure carries a small charge 'q' . An infinite horizontal plane conductor with uniform surface charge density `sigma1 is placed below it . What will be the time period of the pendulum for small amplitude oscillations ?

A

`2pisqrt((L)/((g-(mg)/(epsilon_(0)sigma))))`

B

`sqrt((L)/((g-(mg)/(epsilon_(0)))))`

C

`(1)/(2pi)sqrt((L)/((g-(qsigma)/(epsilon_(0)m))))`

D

`2pisqrt((L)/((g-(qsigma)/(epsilon_(0)m))))`

Text Solution

Verified by Experts

The correct Answer is:
a
In the given situation the electrostatic force acting on the bob is
`F_(e)=Qe` or acceleration `a=(qE)/(m)`
Now effective value of g is
`g_("effective")=g-ag-(qE)/(m)`
`thereforeT=2pisqrt((L)/(g-(qE)/(m)))=2pisqrt((L)/(g-(qsigma)/(epsilon_(0)m)))("using"E=(sigma)/(epsilon_(0)))`
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