An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is

An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is
A. 6.43 cm
B. 8.24 cm
C. 4.26 cm
D. 5.82 cm

Correct Option: Answer is D
r1 = 4.5cm , P1 =is the total pressure on the bubble at a depth of 12m from the surface.

P1 = 12 + 10.34 =22.34m

V1 = 4/3π× r13

= 4/3×π×4.53cm3

P2 = 10.34m
V2 = 4/3πr23
from boyles law:
P1V1 = P2V2

⇒ 22.34× 4/3×π×4.53 = 10.34 × 4/3×π× r23

⇒ 22.34 × 4.53 = 10.34 × r23

⇒ r23= 3√196.88)

⇒ r = 5.82cm

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