Question

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

• A. $3.15\, gm$
• B. $4.51\, gm$
• C. $4.15\, gm$
• D. $1.52\, gm$

Answer 1

Answer: (C)

Volume $V =\frac{4 \pi}{3} r ^{3}=\frac{4 \pi}{3} \times(1)^{3}=4.19 cm ^{3}$
$a =9.8 cm / s ^{2}$
$B - mg = ma$
$m =\frac{ B }{ g + a }$
$m =\frac{\left( V \rho_{\omega} g \right)}{ g + a }=\frac{ V \rho_{\omega}}{1+\frac{ a }{ g }}$
$=\frac{(4.19) \times 1}{1+\frac{9.8}{980}}=\frac{4.19}{1.01}=4.15 gm$