Q. An object weighs $m_{1}$ in a liquid of density $d_{1}$ and that in liquid of density $d_{2}$ is $m_{2}$. The density d of the object is
A) $d = \frac{m_{2}d_{2} - m_{1} - d_{1}}{m_{2} - m_{1}}\ $
B) $d = \frac{m_{1}d_{1} - m_{2} - d_{2}}{m_{2} - m_{1}}$
C) $d = \frac{m_{2}d_{1} - m_{1} - d_{2}}{m_{1} - m_{2}}$
D) $d = \frac{m_{1}d_{2} - m_{2} - d_{1}}{m_{1} - m_{2}}$
Explanation
(d) $V\left( d - d_{1} \right)g = m_{1}g$
$V\left( d - d_{2} \right)g = m_{2}g$
$\frac{d - d_{1}}{d - d_{2}} = \frac{m_{1}}{m_{2}}$
$\therefore\ d = \frac{m_{1}d_{2} - m_{2}d_{1}}{m_{1} - m_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.