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(B) The horizontal range $R$ of water issuing from a small hole at a depth $y$ below the free surface of a liquid in a vessel of total height $H$ is g

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Hole number $3$

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(B) The horizontal range $R$ of water issuing from a small hole at a depth $y$ below the free surface of a liquid in a vessel of total height $H$ is given by $R = 2\sqrt{y(H-y)}$.Here,the total height of the water column is $H = 90 \ cm$.The holes are at heights $h_1 = 20 \ cm, h_2 = 30 \ cm, h_3 = 45 \ cm,$ and $h_4 = 50 \ cm$ from the floor.The depth of each hole from the free surface is $y = H - h$.For hole $1$: $y_1 = 90 - 20 = 70 \ cm$.For hole $2$: $y_2 = 90 - 30 = 60 \ cm$.For hole $3$: $y_3 = 90 - 45 = 45 \ cm$.For hole $4$: $y_4 = 90 - 50 = 40 \ cm$.The horizontal range is maximum when the depth $y$ is equal to half the total height,i.e.,$y = H/2 = 90/2 = 45 \ cm$.Comparing the depths,hole $3$ is at a depth of $45 \ cm$ from the free surface.Therefore,the water falling at the maximum horizontal distance comes from hole $3$.

$A$ cylindrical vessel of $90 \ cm$ height is kept filled up to the brim. It has four holes $1, 2, 3, 4$ which are respectively at heights of $20 \ cm, 30 \ cm, 45 \ cm,$ and $50 \ cm$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from:

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