Question

A body of mass ${}^{\prime }{m}^{\prime }$ expands and its volume increases to two times of its original volume. Then, the density of the body:

• A. Remains constant
• B. Reduces by half
• C. Becomes twice
• D. Becomes thrice

Answer 1

The correct option is B Reduces by half

We know that,

$Density=\frac{Mass}{Volume}$
Let the initial mass and volume be $m$ and $v$ respectively and density be $d_1$.

When the volume is doubled, its density:
$d_2=\frac{m}{2\times v}=\left(\frac{1}{2}\right)\times \frac{m}{v}=\left(\frac{1}{2}\right)\times d_1$

Hence, density of body reduces to half of its initial value when volume of body becomes double keeping the mass constant.