Question

A tank having cross sectional area A has a hole at the bottom of area of cross section $\frac{A}{1000}$. Bottom of the tank is a plane mirror. The tank contains water of refractive index
$\frac{4}{3}$. At the instant, when height of the water in the tank is 5m, a fish is rising vertically in the tank with a velocity
$3\frac{cm}{sec}$ toward the surface.



The velocity with which surface is falling down inside container is

• A. 1 $\frac{m}{s}$
• B. 2 $\frac{m}{s}$
• C. 3$\frac{m}{s}$
• D. 4 $\frac{m}{s}$

Answer 1

The correct option is A 1 $\frac{m}{s}$

Velocity of efflux = $v=\sqrt{2g\times 5}=10\frac{m}{s}$

Velocity of surface = $\frac{10\times \frac{A}{1000}}{A}=1\frac{cm}{s}$