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^2n_1/n_2`
B. `xpiR^2n_2//n_1`
C. `2piR^2n_1//n_2`
D. `piR^2x`

Answer

B

Explanation

Apparent depth
`h_1=(h)/(._(air)n_(liq))=(h)/(n_2//n_1)`
`h=(n_2)/(n_1)h_1`
`(dh)/(dt)=n_2/n_1(dh_1)/(dt)=(n_2)/(n_1)x`
`(dV)/(dt)=piR^2(dh)/(dt)=(n_2/n_1)piR^2x`