Fluid Mechanics

JEE Main level, single correct, medium

133 of 192

Question 133 of 192

A air bubble of radius 1cm1\text{cm} in water has an upward acceleration of 9.8cms–29.8{\text{cms}}^{–2}. The density of water is 1gm cm–31{\text{gm cm}}^{–3} and water offers negligible drag force on the bubble. The mass of the bubble is (g=980cm/s2)\left(g=980\text{cm}/{\text{s}}^{2}\right).

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Answer: (C) 4.15gm4.15\text{gm}

Fb−mg=ma{F}_{b}-mg=ma
Fb=m(g+a){F}_{b}=m\left(g+a\right)
=43πr3ρg=m(g+a)=\dfrac{4}{3}{\pi r}^{3}\rho g=m\left(g+a\right)
m=43π(1)g=m(980+9.8)m=\dfrac{4}{3}\pi \left(1\right)g=m\left(980+9.8\right)
m=4.15m=4.15

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