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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)

Asked in JEE Main 4th Sept 1st Shift 2020 · Floating and submerged bodies

• (1) 3.15 gm
• (2) 1.52 gm
• (3) 4.15 gm
• (4) 4.51 gm

Step-by-step solution

Why the other options are wrong

• (1) comes from no consistent slip lands here; every honest route clusters near the key, since the acceleration is only 1% of g — ignoring the acceleration altogether gives ρ_wV=4.19 gm, still nowhere near 3.15.
• (2) comes from a filler; the volume slips worth checking give 4/3r³=1.33 gm with the π dropped and π r³=3.14 gm with the 4/3 dropped, and neither is 1.52.
• (4) comes from is 4.15 with its last two digits transposed — the copying slip at the final step, and the reason these two options sit next to each other.

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