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$.......gm$
$\left( g =980 \,cm / s ^{2}\right)$
JEE MAIN 2020, Diffcult
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Volume $V =\frac{4 \pi}{3} r ^{3}=\frac{4 \pi}{3} \times(1)^{3}=4.19 cm ^{3}$
$a =9.8 cm / s ^{2}$
$B - mg = ma$
$m =\frac{ B }{ g + a }$
$m =\frac{\left( V \rho_{ \omega} g \right)}{ g + a }=\frac{ V \rho_{ \omega }}{1+\frac{ a }{ g }}$
$=\frac{(4.19) \times 1}{1+\frac{9.8}{980}}=\frac{4.19}{1.01}=4.15 gm$
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