Question

When an air bubble moves up from the bottom of a lake
a) velocity decreases and becomes zero
b) acceleration increases and becomes zero
c) velocity increases and becomes constant
d) acceleration decreases and becomes zero

• A. a, d are correct
• B. a, b are correct
• C. c, d are correct
• D. c is correct

Answer 1

Answer: (C)

c, d are correct

As the bubble rises up, the net forces acting on it are given by-

$ma=V\rho g-mg-f_r$
$⟹ma=V\rho g-Vdg-6\pi \eta rv$

$⟹a=\frac{dv}{dt}=\frac{1}{m}\left(V\right(\rho -d)g-6\pi \eta rv)$

Hence the speed of bubble continuously rises.
However as the speed increases, the frictional force increases and hence the acceleration decreases.