Question

If volume of a steel ball is halved and its mass remains constant, its relative density will be:

• A. same
• B. doubled
• C. halved
• D. can't be determined

Answer 1

Answer: (B)

doubled

Relative density of steel ball is given by

$r=\frac{{\rho }_s}{{\rho }_w}=\frac{m}{V{\rho }_w}$

where, ${\rho }_s$ is the density of ball and ${\rho }_w$ is the density of water

$⟹r\propto \frac{1}{V}$ $(\because m=constant)$

Hence, relative density is inversely proportional to the volume of the ball.

Thus relative density is doubled when the volume of steel ball is halved.