Question

A body is weighed using a spring balance and it reads $5\text{kg}$. When the body is completely immersed in another liquid, the reading on the spring balance changed to $4.8\text{kg}$. If the volume of the body is $200{\text{cm}}^3$, find the density of the liquid.

• A. $2000{\text{kg/m}}^3$
• B. $1000{\text{kg/m}}^3$
• C. $1000{\text{g/cm}}^3$
• D. $1500{\text{kg/m}}^3$

Answer 1

The correct option is B $1000{\text{kg/m}}^3$

Given,
Reading in air = $5\text{kg}$
Weight of the body = $5\times g=50\text{N}$
Reading in liquid = $3\text{kg}$
Apparent weight of the body in liquid = $3\times g=48\text{N}$
Apparent loss in weight = $50-48=2\text{N}$
Therefore, upthrust acting on the body = $2\text{N}={\rho }_l{\text{V}}_{\text{b}}g$

Given, ${\text{V}}_{\text{b}}=200{\text{cm}}^3=200\times {10}^{-6}{\text{m}}^3$

$200\times {10}^{-6}\times {\rho }_l\times g=2$
$\Rightarrow {\rho }_l=\frac{2}{2000\times {10}^{-6}}=1000{\text{kg/m}}^3$