Question

A body of mass 'm' expands and its volume increases to two times its original volume. Density of the body ________.

• A. remains constant
• B. is reduced by half
• C. becomes twice
• D. is reduced to quarter

Answer 1

The correct option is B is reduced by half

Density is given by:
$\rho =\frac{M}{V}$
where:
$M:\text{Mass of body}$
$V:\text{Volume of body}$

Given, new volume is:
$V^{\prime }=2V$

Hence, new density is:
${\rho }^{\prime }=\frac{M}{V^{\prime }}$
${\rho }^{\prime }=\frac{M}{2V}$
${\rho }^{\prime }=\frac{\rho }{2}$

Hence, density reduces by half.