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JEE Main 20127 MayOnline
Exam
JEE Main
Year
2012
Date
7 May
Mode
Online
Subject
Physics
Chapter
Laws of Motion

JEE Main 2012 · 7 May · Online · Physics · Laws of Motion

An engine pumps water continuously through a hose. Water leaves the...

An engine pumps water continuously through a hose. Water leaves the hose with velocity vv and mm is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

Options

  1. Amv3m v^3
  2. Bmv2m v^2
  3. C12mv2\frac{1}{2} m v^2
  4. D12mv3\frac{1}{2} m v^3

Correct answer

B. mv2m v^2

Step-by-step solution

As power P=F.v.=Fℓt\mathrm{P}=F . v .=\frac{F \ell}{t} or, v(Mvt)=F.ℓt⇒Mv2=Fℓℓ⇒F=Mℓv2=mv2[∵Mℓ=m( given  )]\begin{aligned}& \text{ or, }v\left(M \frac{v}{t}\right)=\frac{F . \ell}{t}\\ & \Rightarrow \quad M v²=F \ell \ell \\ & \Rightarrow \quad F=\frac{M}{\ell}v^2=m v² \\ & {\left[\because \frac{M}{\ell}=m(\text{\text{ given } })\right]} \end{aligned}
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