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SSC JE ME Previous Paper 3 (Held on: 27 Sep 2019 Evening)

Option 1 : ρaV^{2}

ST 1: General Knowledge

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20 Questions
20 Marks
20 Mins

**Explanation:**

**Jet Striking a stationary vertical plate:**

**From Newton’s second law**

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

∴ \(F = \frac{{\left( {initial\;momentum\; - \;final\;momentum} \right)}}{{time}}\)

∴ \(F = \frac{{\left( {mass\; \times \;initial\;velocity\; - \;mass\; \times \;final\;velocity} \right)}}{{time}}\)

∴ \(F = \frac{{m\;\left( {velocity\;of\;jet\;before\;striking - velocity\;of\;jet\;after\;striking} \right)}}{{time}}\)

∴ \(F = \frac{{m\left( {V - 0} \right)}}{{time}}\) ----(1)

Now

**Mass =ρ × volume ; volume = area × length**

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

∴ \(\frac{m}{{time}} = \rho \times area \times velocity\) ----(2)

Substitute equation (2) in equation (1)

**∴ F = ρ × a × v ^{2}**

**Note: Jet Striking a Stationary incline plate**

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

\(\begin{array}{l} {F_n} = \rho aV\left( {Vsin\theta - 0} \right) = \rho a{V^2}\sin \theta \\ {F_x} = {F_n}\sin \theta = \rho {V^2}\sin \theta \times \sin \theta = \rho a{V^2}{\sin ^2}\theta \\ {F_y} = {F_n}\cos \theta = \rho {V^2}\sin \theta \times \cos \theta = \rho a{V^2}{\sin ^2}\theta \cos \theta \end{array}\)