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Q.

The apparent depth of water in cylindrical water tank of diameter 2-R cm is reducing at the rate of x cm/min when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is (n1 = refractive index of air, n2 = refractive index of water)

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a

xπR2n1/n2

b

xπR2n2/n1

c

2πRn1/n2

d

πR2x

answer is B.

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Detailed Solution

Apparent depth h'=h airμliquid⇒dh'dt=1 aμwdhdt⇒x=1 aμwdhdt⇒dhdt=aμwxNow volume of water V=πR2h⇒dVdt=πR2dhdt=πR2.aμwx=aμwπR2x=μwμoπR2x=n2n1πR2x

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The apparent depth of water in cylindrical water tank of diameter 2-R cm is reducing at the rate of x cm/min when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is (n1 = refractive index of air, n2 = refractive index of water)