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Question

Two pith balls carrying identical charges are suspended from a common point by strings of equal lengths, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now will be :


A
r21/3
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B
2r3
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C
2r3
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D
(12)2
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Solution

The correct option is A r21/3

Let m be the mass of each ball and q be the charge on each ball.

Force of repulsion, F=14πϵ0q2r2

In equilibrium,

Tcosθ=mg (1)
Tsinθ=F (2)

From (1) and (2) , we get,

tan θ=Fmg=14πϵ0q2r2mg

From figure (a),

(r2)y=14πϵ0q2r2mg (3)

From figure (b)


(r2)y2=14πϵ0q2r 2mg(4)

From (3) and (4), we get

2rr=r2r2r3=r32r=r21/3

Hence, option (d) is the correct answer.

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