The apparent depth of water in cylindrical water tank of diameter `2R 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 `(n_(1)=` refractive index of air, `n_(2)=` refractive index of water )

Options

A. `(xpiR^(2)mu_(1))/(mu_(2))`
B. `(xpiR^(2)mu_(2))/(mu_(1))`
C. `(2piRmu_(1))/(mu_(2))`
D. `piR^(2)x`

Answer

B

Explanation

`(mu_(2))/(mu_(1))=(real depth)/(apparent depth)`
`"change in" depth=(mu_(2))/(mu_(1))xx "change in" apparent depth`
`(dh)/(dt)=(mu_(2))/(mu_(1))x cm min^(-1)`
The amount of water drained in cc per minute
`=(dh)/(dt)xxpiR^(2)=xpiR^(2)(mu_(2))/(mu_(1))`