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An engine pumps water continously throug...

An engine pumps water continously through a hose. Water leave the hose with a velocity `v` and `m` is the mass per unit length of the Water jet. What is the rate at Which kinetic energy is imparted to water?

A

`(1)/(2) m_(0)v^(3)`

B

`(1)/(2) m_(0)v^(2)`

C

`(1)/(2)m_(0) v^(3//2)`

D

`(1)/(2)m_(0)v^(1//2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`m_(0)=(dm)/(dx)`
`(d)/(dn) (KE)=(d)/(dt)((1)/(2)mv^(2))=(1)/(2) ((dm)/(dt))v^(2)`
=`(1)/(2)((dm)/(dx))((dx)/(dt))v^(2)=(1)/(2)m_(0)v^(3)`.
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Knowledge Check

  • An engine pumps water continously through a hole. Peeds with which water pases through the hole nozzle is v and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is eing imparted to the water.

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