Question

A cylindrical drum, open at the top, contains 30 litres of water. It drains out through a small opening at the bottom. 10 litres of water comes out in time t₁, the next 10 litres in a further time t₂and the last 10 litres in a further time t₃. Then,

• A. (a) t₁ = t₂ = t₃
• A. (b) t₁ "> t₂ "> t₃
• A. (c) t₁ < t₂ < t₃
• A. (d) t₂ "> t₁ = t₃

Answer 1

(c)

Velocity of efflux, v = $\sqrt{2gx}$, where x = height of liquid.

As the water drains out, x reduces, and hence, v reduce. This reduces the rate of drainage. Hence, it requires a longer time to drain the same volume of water.