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(D) The rate of flow of water (volume per second) is given by the equation of continuity: $Q = A v$.According to Torricelli's Law,the velocity of effl

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$\frac{L}{\sqrt{2\pi}}$

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(D) The rate of flow of water (volume per second) is given by the equation of continuity: $Q = A v$.According to Torricelli's Law,the velocity of efflux at a depth $h$ is $v = \sqrt{2gh}$.For the square hole: Area $A_1 = L^2$,depth $h_1 = y$. So,$v_1 = \sqrt{2gy}$.The flow rate $Q_1 = A_1 v_1 = L^2 \sqrt{2gy}$.For the circular hole: Area $A_2 = \pi R^2$,depth $h_2 = 4y$. So,$v_2 = \sqrt{2g(4y)} = 2\sqrt{2gy}$.The flow rate $Q_2 = A_2 v_2 = \pi R^2 (2\sqrt{2gy})$.Given that the flow rates are equal,$Q_1 = Q_2$:$L^2 \sqrt{2gy} = 2\pi R^2 \sqrt{2gy}$.Dividing both sides by $\sqrt{2gy}$,we get $L^2 = 2\pi R^2$.Solving for $R$,we get $R^2 = \frac{L^2}{2\pi}$,which implies $R = \frac{L}{\sqrt{2\pi}}$.

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