JEE PYQ: Mechanical Properties Of Fluids Question 13
Question 13 - 2020 (04 Sep 2020 Shift 1)
An 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 ($g = 980$ cm/s$^2$):
(1) 4.51 gm
(2) 3.15 gm
(3) 4.15 gm
(4) 1.52 gm
Show Answer
Answer: (3) 4.15 gm
Solution
Given: Radius of air bubble = 1 cm, Upward acceleration, $a = 9.8$ cm/s$^2$, $\rho_{\text{water}} = 1$ g cm$^{-3}$ Volume $V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi(1)^3 = 4.19$ cm$^3$
$F_{\text{buoyant}} - mg = ma \Rightarrow m = \frac{F_{\text{buoyant}}}{g + a}$ $\therefore m = \frac{V\rho_w g}{g + a} = \frac{(4.19) \times 1}{1 + \frac{9.8}{980}} = \frac{4.19}{1.01} \approx 4.15$ g
BETA
