Question

A solid block of material density 6000 $kg/m^3$ weighs 10 kg wt. in air. When it is immersed completely into a liquid, it weighs 6 kg wt. What is the density of the liquid?

• A.
  $2200kg/m^3$
• B.
  $2400kg/m^3$
• C.
  $1200kg/m^3$
• D.
  $600kg/m^3$

Answer 1

The correct option is B

$2400kg/m^3$
Density of solid block, ${\rho }_b=6000kg/m^3$

Weight of solid block, $W_b=10kgwt.$

Mass of solid block, $M_b=10kg$

Volume of solid block, $V=\frac{Mass}{Density}=\frac{M_b}{{\rho }_b}\Rightarrow V=\frac{10}{6000}=\frac{1}{6}\times {10}^{-2}{m}^3$

Weight of liquid displaced = Upthrust on the solid block

Now, upthrust on the solid block $=(10–6)g=4g\Rightarrow {\rho }_1\times V\times g=4g(\because \text{mass of liquid}={\rho }_1\times V)\Rightarrow {\rho }_1=\frac{4}{V}\Rightarrow {\rho }_1=\frac{4}{\frac{1}{6}\times {10}^{-2}}=24\times {10}^2\Rightarrow {\rho }_1=2400kg/m^3$

Hence, the correct answer is option (b).