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Two identical charged spheres ore suspended by strings of equa

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Two identical charged spheres ore suspended by strings of equal lengths. The strings make an angle of $3 0^{\circ}$ with each other. When suspended in a liquid of density $0.8 g cm^{3}$ , the angle remains the same. If density of the material of the sphere is $1.6 g cm^{- 3}$ , the dielectric constant of the liquid is :

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Updated on: Nov 8, 2023

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Two identical charged spheres ore suspended by strings of equal lengths. The strings make an angle of

3 0^{\circ}

with each other. When suspended in a liquid of density

0.8 g cm^{3}

, the angle remains the same. If density of the material of the sphere is

1.6 g cm^{- 3}

, the dielectric constant of the liquid is :

15 mins ago

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15 mins ago

Text solutionVerified

From free body diagram,
Solution Image

F_{e} = T sin 1 5^{\circ} \dots\dots (1)

m g = T cos 1 5^{\circ} \dots\dots (2)

from eq(1) and (2)

tan 1 5^{\circ} = \frac{F _{e}}{m g} \dots\dots\dots ..

(i)

In liquid,

F_{e}^{'} = T sin 1 5^{\circ} \dots\dots

(3)

m g = F_{B} + T cos 1 5^{\circ} \dots\dots (4)

Where

F_{B}

is buoyant force.

F_{B} = V (d - σ) g = V (1.6 - 0.8) g = 0.8 V g

From,

V = \frac{ma ss}{d e n s i t y} \Rightarrow V = \frac{m}{d}

F_{B} = V (d - σ) g = V (1.6 - 0.8) g = 0.8 \frac{m _{d}}{d} g

0.8 \frac{m}{d} g = 0.8 \frac{m}{1.6} g = \frac{m g}{2}

putting value in eq(4)

mg

= F_{B} + T cos 1 5^{\circ} \Rightarrow m g = \frac{m g}{2} + T cos 1 5^{\circ}

\frac{m g}{2} = T cos 1 5^{\circ} \dots . \dots . (5)

from eq(3) and eq(5)

tan

1 5^{\circ} = \frac{F _{e}^{'}}{\frac{m g}{2}} = \frac{2 F _{e}^{'}}{m g} \dots .. (6)

Step 2: Equating the equations:

From eq(6) and (i)

\frac{F _{e}}{m g} = \frac{2 F _{e}^{'}}{m g} \Rightarrow F_{e} = 2 F_{e}^{'}

F_{e}^{'} = \frac{F _{e}}{2}

From columb's force of electrostatic in air and liquid:

\frac{q ^{2}}{4 π ε _{0} r ^{2} \times K} = \frac{q ^{2}}{4 π ε _{0} r ^{2} \times 2}

K=2

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Question Text	Two identical charged spheres ore suspended by strings of equal lengths. The strings make an angle of $3 0^{\circ}$ with each other. When suspended in a liquid of density $0.8 g cm^{3}$ , the angle remains the same. If density of the material of the sphere is $1.6 g cm^{- 3}$ , the dielectric constant of the liquid is :
Updated On	Nov 8, 2023
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 19
Upvotes	1896
Avg. Video Duration	10 min

Text solutionVerified

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