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5.work,energy,power and collision — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
MCQ
An engine pump is used to pump a liquid of density $\rho $ continuously through a pipe of cross-sectional area $A$. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
  • ✓
    $\frac{1}{2}A\rho {v^3}$
  • B
    $\frac{1}{2}A\rho {v^2}$
  • C
    $\frac{1}{2}A\rho v$
  • D
    $A\rho v$
✓

Answer

Correct option: A.
$\frac{1}{2}A\rho {v^3}$
a
(a)Energy supplied to liquid per second by the pump = $\frac{1}{2}\frac{{m{v^2}}}{t}$= $\frac{1}{2}\frac{{V\rho {v^2}}}{t}$

= $\frac{1}{2}A \times \left( {\frac{l}{t}} \right) \times \rho \times {v^2}$$\left[ {\frac{l}{t} = v} \right]$

$ = \frac{1}{2}A \times v \times \rho \times {v^2}$= $\frac{1}{2}A\rho {v^3}$

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