Answer
The mass of the bubble is $~~5.12\times 10^{-7}~kg$
Work Step by Step
The buoyant force is equal to the weight of the water that is displaced by the bubble.
We can find the buoyant force:
$F_b = mg$
$F_b = \rho~V~g$
$F_b = \rho~\frac{4}{3}\pi~r^3~g$
$F_b = (1000~kg/m^3)~(\frac{4}{3}\pi)~(0.500\times 10^{-3}~m)^3(9.8~m/s^2)$
$F_b = 5.131\times 10^{-6}~N$
We can find the mass of the bubble:
$\sum~F = ma$
$F_b-mg = ma$
$F_b = m(g+a)$
$m = \frac{F_b}{g+a}$
$m = \frac{5.131\times 10^{-6}~N}{9.8~m/s^2+0.225~m/s^2}$
$m = 5.12\times 10^{-7}~kg$
The mass of the bubble is $~~5.12\times 10^{-7}~kg$
