The force exerted by a jet of water on a stationary vertical plate in the direction of the jet is ________.

where, ρ = mass density of the liquid, a = cross-sectional area of the jet, V = velocity of the jet.

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SSC JE ME Previous Paper 9 (Held on: 27 Sep 2019 Evening)
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  1. ρaV2
  2. ρaV
  3. ρa2V
  4. ρaV3

Answer (Detailed Solution Below)

Option 1 : ρaV2
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Detailed Solution

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Explanation:

Jet Striking a stationary vertical plate:

From Newton’s second law

F = dp/dt; where; p = momentum = mv

∴ 

∴ 

∴ 

∴        ----(1)

Now

Mass = ρ × volume ; volume = area × length

∴ [mass (m)]/time = [ρ × area × length]/time ∵ length/time = velocity

       ----(2)

Substitute equation (2) in equation (1)

∴ F = ρ × a × v2

 

Note: Jet Striking a Stationary incline plate

Let us apply the impulse-momentum equation in the direction normal to the plate 

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