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Two identical tennis balls each having m...

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle `'theta'` with the vertical ?

A

`x=((q^(2)l^(2))/(2piepsilon_(0)m^(2)g^(2)))^(1/3)`

B

`x=((q^(2)l)/(2piepsilon_(0)mg))^(1/2)`

C

`x=((q^(2)l^(2))/(2piepsilon_(0)m^(2)g))^(1/3)`

D

`x=((q^(2)l)/(2piepsilon_(0)mg))^(1/3)`

Text Solution

Verified by Experts

The correct Answer is:
D

Force due to charge `=(kq^(2))/(x^(2))`
`tantheta=((kq^(2))/(x^(2)))/(mg)~~sintheta`
`implies (kq^(2))/(mgx^(2))=(x)/(2l)impliesx^(3)=(2kq^(2)l)/(mg)`
`impliesx=((2kq^(2)l)/(mg))^(1//3)`
`implies x=((2q^(2)l)/(4piepsilon_(0)mg))^(1//3)=((q^(2)l)/(2piepsilon_(0)mg))^(1//3)`
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