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Question: Two solids A and B float in water. It is observed that A floats with \(\frac { 1 } { 4 }\) of its vo...

Two solids A and B float in water. It is observed that A floats with 14\frac { 1 } { 4 } of its volume above the water level. The ratio of the density of A to that of B is

A

4 : 3

B

2 : 3

C

3 : 4

D

1 : 2

Answer

2 : 3

Explanation

Solution

Upthrust = weight of body

For A, VA2×ρW×g=VA×ρA×g⇒ρA=ρW2\frac { V _ { A } } { 2 } \times \rho _ { W } \times g = V _ { A } \times \rho _ { A } \times g \Rightarrow \rho _ { A } = \frac { \rho _ { W } } { 2 }

For B, 34VB×ρW×g=VB×ρB×g⇒ρB=34ρW\frac { 3 } { 4 } V _ { B } \times \rho _ { W } \times g = V _ { B } \times \rho _ { B } \times g \Rightarrow \rho _ { B } = \frac { 3 } { 4 } \rho _ { W }

(Since 1/4 of volume of B is above the water surface)

∴ ρAρB=ρW/23/4ρW=23\frac { \rho _ { A } } { \rho _ { B } } = \frac { \rho _ { W } / 2 } { 3 / 4 \rho _ { W } } = \frac { 2 } { 3 }