JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Fluid Mechanics

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is

528

^{3}

(dm: decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ______ cm.

(A) $1202$
(B) $1402$ ✓ Correct
(C) $1403$
(D) $1203$

Answer: (B)

Solution

The water height follows from the capacity,

h = \frac{V}{π r ^{2}} = \frac{0.528}{π ( 0.4 ) ^{2}} = 1.05 m = 105 cm

, which is also the vessel height. The hole is

70 cm

below the surface, hence

35 cm

above the vessel base; standing on a block of the same height, the hole is

105 + 35 = 140 cm

above the ground. The efflux speed is

v = 2 g h_{w} = 2 \times 10 \times 0.70 = 14 m/s

, and the time to fall

H = 1.40 m

t = \frac{2 H}{g} = \frac{2 \times 1.40}{10} = 0.28 s

. The horizontal range is

R = v t = 14 \times 0.28 = 3.92 \approx 1.98 m = 1402 cm

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Fluid Mechanics

Solution

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