Physics - Fluid Question with Solution | TestHub

Let the volume of the body be $V$.

The downward gravitational force acting on the body is $W=V\rho g$.

The upward buoyant force exerted by the water is $F_B=V{\rho }^{\prime }g$.

The net downward force on the body is $F_{net}=W-F_B=Vg(\rho -{\rho }^{\prime })$.

The downward acceleration $a$ of the body is given by $a=\frac{F_{net}}{m}=\frac{Vg(\rho -{\rho }^{\prime })}{V\rho }=\frac{g(\rho -{\rho }^{\prime })}{\rho }$.

Using the second equation of motion $s=ut+\frac{1}{2}a{t}^2$ with initial velocity $u=0$ and distance $s=d$:

$d=\frac{1}{2}a{t}^2$

$t=\sqrt{\frac{2d}{a}}$

Substituting the value of $a$:

$t={\left[\frac{2d\rho }{g(\rho -{\rho }^{\prime })}\right]}^{\frac{1}{2}}$

Answer: ${\left[\frac{2d\rho }{g(\rho -{\rho }^{\prime })}\right]}^{\frac{1}{2}}$