# Question #7dd19

May 29, 2017

To choose the correct option we are to analyse the forces acting on the bubble .

Let the volume of the bubble at the certain instant be $V$.

The mass of the gaseous material in the bubble be $m$.

The downward gravitational pull on it will be $F \downarrow = m g = V \mathrm{dg}$, where $d =$ density of the gaseous material of the bubble.

The upward buoyant force on it at the inatant considered will be $F \uparrow = V \rho g$, where $\rho =$ density of boiling water.

We know that $\rho > d$

Hence $F \uparrow > F \downarrow$

So net force acting at that instant ${F}_{N} = F \uparrow - F \downarrow > 0$

Hence the positive acceleration of the bubble at that instant will be $a = {F}_{N} / \left(V d\right) = \frac{\rho - d}{d}$

So option (a) is correct.