A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at a maximum horizontal distance, then the depth of the hole from the free surface must be

Question

A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at a maximum horizontal distance, then the depth of the hole from the free surface must be, 3 4 H, 2 3 H, 1 4 H, 1 2 H

MARKS App · Accepted Answer

As hole is made in the tank below the free surface of water, so water rushing from this hole follows a parabolic path. The velocity of efflux liquid, v = 2 gh Time, t = 2 H - h g Horizontal range, R = vt R = 2 gh × 2 H - h g 1 2 ie , R 2 = 4 h H - h = 4 Hh - h 2 The range is maximum if dR dh = 0 or 2 RdR dh = 4 H - 2 h or 0 = H - 2 h or h = H 2

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