Question

A block of wood floats in water with of its volume submerged. If the same block just floats in a liquid, the density of the liquid (in kg ) is

• A. 1250
• B. 600
• C. 400
• D. 800

Answer 1

Answer: (D)

800

Answer 2

According to Archimedes’s principle

Weight of the body = Weight of the liquid displaced

Let V be volume of block.

In water,

……. (i)

In liquid

$\rho _ { \text {block } } = \rho _ { \text {liquid } }$ ……… (ii)

From (i) and (ii), we get

$\rho _ { \text {Liquid } } \frac { 4 } { 5 } \rho _ { \text {water } } = \frac { 4 } { 5 } \times 10 ^ { 3 } \mathrm {~kg} \mathrm {~m} ^ { - 3 }$

$= 800 \mathrm {~kg} \mathrm {~m} ^ { - 3 }$