Question

The apparent depth of water in a 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 $cc/minute$ is: ($n_1$ = refractive index of air, $n_2$ = refractive index of water)

• A. $\frac{x\pi R^2{n}_1}{n_2}$
• B. $\frac{x\pi R^2{n}_2}{n_1}$
• C. $\frac{2\pi R^{}{n}_1}{n_2}$
• D. $\pi R^{2}x$

Answer 1

The correct option is B $\frac{x\pi R^2{n}_2}{n_1}$

We know that

$\frac{RealDepth}{Apparentdepth}=\frac{n_2}{n_1}$

$\Rightarrow$Real Depth$=\left(\frac{n_2}{n_1}\right)$ Apparent Depth

Rate of change in real depth $=\left(\frac{n_2}{n_1}\right)$ rate of change in apparent depth

$=\left(\frac{n_2}{n_1}\right)x$

$\frac{dv}{dt}=\frac{d\left(A\right)h}{dt}=\frac{Adh}{dt}=\left[n{\left(R\right)}^2\right]\left[\frac{n_2}{n_1}x\right]$

Option $B$ is correct