Question

A small spherical ball of density p is gently released in a liquid of density s(p>s). Find the initial acceleration of the ball?

Answer 1

The forces acting on the spherical ball would be the buoyant force and weight.

so $W-F=ma$.

Now $F$ = buoyant force = $sVg$

Where $V$ = volume of the spherical ball

Also, $W=mg$

Now, $mg-sVg=ma$......(1)

We know that mass is density times volume so $m=pV$

Putting in(1)

$PVg-sVg=ma$

$(p-s)Vg=ma$

Also, $V=\frac{m}{p}$

$(p-s)\frac{mg}{p}=ma$

So $a=(p-s)\frac{g}{p}$