First slide

Pressure in a fluid-mechanical properties of fluids

Question

A air bubble of radius 1 cm in water has an upward acceleration $9.8 c m s^{- 2}$ . The density of water is 1 gm $c m^{- 3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $(g = 980 c m / s^{2})$

Moderate

A

3.15 gm
B

4.15 gm
C

4.51 gm
D

1.52 gm

Solution

Buoyant force dominates weight.
So acceleration $a = \frac{F_{B} - m g}{m}$
$\frac{F_{B}}{m} = a + 5 = 989.8 c m / s^{2}$
Also $F_{B} = V ρ_{l i q} g$
$\Rightarrow (m) 989.8 = \frac{4}{3} π {(1)}^{3} (1) (980)$
So $m = \frac{(\frac{4 π}{3}) (980)}{989.8} = 4.145 g m$ =4.15 gm nearly

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