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JEE Main 2020 (4 Sep, Shift 1) · Archimedes' Principle & Floatation

Archimedes' Principle & Floatation question from JEE Main 2020 (4 Sep, Shift 1)

Q17JEE Main 2020 · 4 SEP · SHIFT 1Difficult

Archimedes' Principle & Floatation

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 (g = 980 cm/s2).

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Answer: (d)

Newton's law for the bubble: $V\rho_w g - mg = ma \Rightarrow m = \dfrac{V\rho_w g}{g + a}$ .
$V = \dfrac{4}{3}\pi(1)^3 = 4.19$ cm $^{3}$
$m = \dfrac{4.19 \times 1 \times 980}{980 + 9.8} = \dfrac{4.19}{1.01} \approx 4.15$ g
So the answer is (d) 4.15 gm.

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