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An air bubble of radius 4.5 cm initially at a depth of 12...

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 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 = 43π× r31

= \frac{4}{3}× π×{4.5^3cm^3}

P_2 = 10.34m

V_2  = \frac{4}{3} {π}{r^3_2}

from boyles law:

P_1V_1  = P_2V_2 

⇒ 22.34× \frac{4}{3}× π×{4.5^3} = 10.34 × \frac{4}{3}×π×{r^3_2}

⇒ 22.34 × 4.5^3 = 10.34 × r^3_2

 r^3_2 = \sqrt[3]{196.88}

⇒ r_2 = 5.82cm