A pressure-pump has a horizontal tube of cross-sectional area $10 \mathrm{~cm}^{2}$ for the outflow of water at a speed of $20 \mathrm{~m} / \mathrm{s}$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ ]

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Conservation of Momentum

A pressure-pump has a horizontal tube of cross-sectional area

10 cm^{2}

for the outflow of water at a speed of

20 m / s

. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water

= 1000 kg / m^{3}

]

(A)300 N
(B)500 N
(C)250 N
(D)400 N✓ Correct

Answer: (D)

Solution

The force exerted by the water jet on the wall is given by

F = ρ a v^{2}

, where

ρ

is density,

a

is cross-sectional area, and

v

is velocity. Substituting:

F = 1 0^{3} \times 10 \times 1 0^{- 4} \times 20 \times 20 = 400

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Single correct option

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