A bubble is at the bottom of the lake of depth h . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to l metre of water column, then h is equal to

Question

A bubble is at the bottom of the lake of depth h . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to l metre of water column, then h is equal to, 26 l, l, 25 l, 30 l

MARKS App · Accepted Answer

From Boyle's law p V = constant ∴ p 1 V 1 = p 2 V 2 Here, p 1 = ρ g h + l , V 1 = 4 3 π r 3 p 2 = ρ g l , V 2 = 4 3 π ( 3 r ) 3 ∴ h + l 4 3 π r 3 = l × 4 3 π 3 r 3 or h + l = 27 l ∴ h = 26 l

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