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)n_(1))/n_(2)`
B. `(xpiR^(2)n_(2))/n_(1)`
C. `(2piRn_(1))/n_(2)`
D. `piR^(2)x`

Answer

B

Explanation

(b) As `y_(a)=((n_(1)/(n_(2)))y`
Here, y= actual depth
and `y_(a)`=apparent depth
`therefore y=(n_(1)/(n_(2)))cdoty_(a)rArr(-(dy)/(dt))=(n_(2))/(n_(1))(-(dy_(a))/(dt))=(n_(2)x) /(n_(1))`
`(dv)/(dt)=Acdot(-(dy)/(dt))=(piR^(2)n_(2)x)/n_(1)`