Question

suppose you and two othe people are underwatr when the other two people simultaneously exhale. one of them releases a large bubble and the other releases a small bubble. you observe that both bubbles begin to rise with identical accelerations. thoroughly, and with adequate detail explain your observation. ( interestingly, the bubbles will continue to rise with nearly identical motions, but you are only required to explain the original acceleration)

Answer 1

For any bubble under water :

Let m = mass, V = volume, a = upward acceleration, F_B = buoyant force, W = weight.

Its equation of motion is : F_B - W = m x a

or, (V x d_w x g) - (m x g) = m x a , where d_w = density of water.

or,   

or,

or,   

or,    , (d_a = density of air exhaled)

Since d_w , d_a and g are all constants, so we see that the upward acceleration of the bubble is constant and it does not depend on the size of the bubble. Hence, both the bigger bubble and the smaller bubble will rise upward with the same acceleration.