Question

The area of two holes A and B are 2a and a respectively. The holes are at height $\left(\frac{H}{3}\right)and\left(\frac{2H}{3}\right)$ from surface of water. Correct option(s) is/are

• A. The velocity of efflux at hole B is 2 times the velocity of efflux at hole A.
• B. The velocity of efflux at hole B is $\sqrt{2}$ times the velocity of efflux at hole A.
• C. The discharge is same through both the holes.
• D. The discharge through hole A is $\sqrt{2}$ times the discharge through hole B.

Answer 1

Answer: (B), (D)

The correct options are
B The velocity of efflux at hole B is $\sqrt{2}$ times the velocity of efflux at hole A.
D The discharge through hole A is $\sqrt{2}$ times the discharge through hole B.

$V_A=\sqrt{\frac{2gH}{3}},V_B=\sqrt{\frac{4gH}{3}}=\sqrt{2}{\left(\frac{2gH}{3}\right)}^{\frac{1}{2}}=\sqrt{2}{V}_A{Q}_A=V_A\left(2a\right)\&Q_B=V_B\left(a\right)=V_A\left(\sqrt{2}a\right)\frac{Q_A}{Q_B}=\sqrt{2}$