Question:

An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ 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

Updated On: Mar 23, 2023
  • $mv^3$
  • $mv^2$
  • $\frac{1}{2}mv^{2}$
  • $\frac{1}{2}mv^{3}$
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The Correct Option is D

Solution and Explanation

Rate of kinetic energy $$ KE =\frac{ d }{ dt } \frac{1}{2} Mv ^{2} $$ But $\quad M = mL$ $$ KE =\frac{1}{2} \frac{ dm }{ dt } Lv ^{2}=\frac{1}{2} mv ^{3} $$
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Concepts Used:

Kinetic energy

Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.