Question

Two identical balls each having a density 1.6 gcm^–3 are suspended from a common point by two insulating strings of equal length. Both the balls have equal mass and charge. In equilibrium each string makes an angle 30° with vertical. Now both the balls are immersed in a liquid of density 0.8 gcm^–3, but the angle does not change. The dielectric constant of the liquid is-

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

In the liquid,

F_e' = and W' = W – up thrust

Applying Lami's theorem,

In Vacuum, $\frac { W } { \sin ( 90 + 30 ) }$ =

or $\frac { \mathrm { W } } { \cos 30 ^ { \circ } }$ = $\frac { \mathrm { F } _ { \mathrm { e } } } { \sin 30 ^ { \circ } }$ ………..(1)

In liquid = $\frac { \mathrm { F } _ { \mathrm { e } } { } ^ { \prime } } { \sin 30 ^ { \circ } }$ ……...(2)

\ $\frac { \mathrm { W } } { \mathrm { W } ^ { \prime } }$ = or K =

= $\frac { \rho _ { \mathrm { s } } } { \rho _ { \mathrm { s } } - \rho _ { \ell } }$ = $\frac { 1.6 } { 1.6 - 0.8 }$ = 2