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The area of two holes $A$ and $B$ are $2 a$ and $a$ respectively. The holes are at depths $(H / 3)$ and $(2 H / 3)$ from surface of water

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The discharge through hole $A$ is $\sqrt{2}$ times the discharge through hole $B$ .

The velocity of efflux at hole $B$ is $2$ times the velocity of efflux at hole $A$

The velocity of efflux at hole $B$ is $\sqrt{2}$ times the velocity of efflux at hole $A$

The discharge is same through both the holes

answer is B, D.

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Detailed Solution

$V_{A} = {(2 g \frac{H}{3})}^{1 / 2}; V_{B} = {(\frac{4 g H}{3})}^{1 / 2} V_{B} = \sqrt{2} {(\frac{2 g H}{3})}^{1 / 2} = \sqrt{2} V_{A}; Q_{A} = V_{A} (2 a) a n d Q_{B} = V_{B} (a)$

Therefore $\frac{Q_{A}}{Q_{B}} = \sqrt{2}$

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