In a cylindrical vessel containing liquid of density ρ, there are two holes in the side walls at heights of h₁ and h₂ respectively such that the range of efflux at the bottom of the vessel is same. Find the height of a hole, for which the range of efflux would be maximum.
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Question

In a cylindrical vessel containing liquid of density ρ, there are two holes in the side walls at heights of h₁ and h₂ respectively such that the range of efflux at the bottom of the vessel is same. Find the height of a hole, for which the range of efflux would be maximum.

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G1 Physics · Accepted Answer

Step 1: If the liquid surface is at height H above the bottom, the horizontal range from a hole at height y is R = 2√[y(H−y)]. Equal ranges for holes at h₁ and h₂ imply h₁+h₂ = H. Step 2: Range is maximum at y = H/2. Hence y = (h₁+h₂)/2. Correct answer: C.