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Q.

A bubble of radius r is made of a soap solution at one end of a long capillary tube,  other  end of which is closed. Assuming Air is non-viscous and its flow in the capillary is  laminar and the process is slow enough to regard it a quasi-static one and disregard  effects of viscosity and time required for liquid in the wall of the bubble to readjust its shape, 
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time interval taken to deflate the bubble (through a small opening at other end of  capillary tube) from an initial radius  R0 to a final radius R is proportional to  R0nRn ,  then n is  _____

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answer is 3.5.

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Detailed Solution

apply Bernoulli’s principle

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A bubble of radius r is made of a soap solution at one end of a long capillary tube,  other  end of which is closed. Assuming Air is non-viscous and its flow in the capillary is  laminar and the process is slow enough to regard it a quasi-static one and disregard  effects of viscosity and time required for liquid in the wall of the bubble to readjust its shape, time interval taken to deflate the bubble (through a small opening at other end of  capillary tube) from an initial radius  R0 to a final radius R is proportional to  R0n−Rn ,  then n is  _____