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Question

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30 with each other. When suspended in a liquid of density 0.8 g /cm3, the angle remains the same. If density of the marterial of the sphere is 1.6 g /cm3, then dielectric constant of the liquid is

A
4
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B
3
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C
2
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D
1
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Solution

The correct option is C 2
From free body diagram,

Fe=T sin 15.....(i)
mg=T cos 15.....(ii)
from equation (i) and (ii),
tan 15=Femg....(iii)

In liquid, Fe=Tsin15...(iv)
mg=FB+T' cos 15....(v)
Where FB is buoyant force.
FB=V(dρ)g=V(1.60.8)g=0.8Vg
[FB=VρgandV=massdensity]
=0.8mdg=0.8mg1.6=mg2
put the value of FB in equation (v),
mg2=Tcos 15....(vii)
From equation (iv) and (vii),
tan15=2Femg......(ii)
from (i) and (ii),
Femg=2FemgFe=2Fe
Fe=Fe2
By the formula of force,
q24ρϵ0K=q24ρϵ0×2

K=2

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