Question

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

• A. $\text{4.51 gm}$
• B. $\text{3.15 gm}$
• C. $\text{4.15 gm}$
• D. $\text{1.52 gm}$

Answer 1

The correct option is C $\text{4.15 gm}$

Given, $r=1\text{cm};a=9.8{\text{cm s}}^{-2}{\rho }_w=1{\text{g cm}}^{-3};g=980{\text{cm s}}^{-2}$


Volume, $V=\frac{4\pi r^3}{3}=\frac{4\pi }{3}\times (1{)}^3=4.19{\text{cm}}^3$
$F_{buoyant}-mg=ma$
$\Rightarrow m=\frac{F_{buoyant}}{g+a}$

$\therefore m=\frac{V{\rho }_{\omega }g}{g+a}=\frac{V{\rho }_{\omega }}{1+\frac{a}{g}}$

$=\frac{\left(4.19\right)\times 1}{1+\frac{9.8}{980}}=\frac{4.19}{1.01}\approx 4.15\text{g}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.