An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is - Physics MCQ Physics | ExamTest.live

hardMCQPhysicsPhysics

1 mark

An engine pumps water continuously through a hose. Water leaves 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 $m v^{2}$
B $\frac{1}{2} m v^{2}$
C $\frac{1}{2} m^{2} v^{2}$
D $\frac{1}{2} m v^{3}$

Solution & Step-by-step Explanation

Rate of imparting kinetic energy is Power (P). P = \frac{d ( K E )}{d t} = \frac{d}{d t} (\frac{1}{2} M v^{2}) Assuming v is constant: P = \frac{1}{2} v^{2} \frac{d M}{d t} We are given m as mass per unit length (m = \frac{d M}{d x}).The rate of mass flow \frac{d M}{d t} = \frac{d M}{d x} \cdot \frac{d x}{d t} = m \cdot v .Substituting this into the power equation: P = \frac{1}{2} v^{2} (m v) = \frac{1}{2} m v^{3}

Practice this question

Try it yourself before checking the explanation above.

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

m v^{2}

\frac{1}{2} m v^{2}

\frac{1}{2} m^{2} v^{2}

\frac{1}{2} m v^{3}

Share This Question

Mechanics Work Power Energy Fluid Dynamics

Related Questions

mediumMCQ

Consider a water tank as shown in the figure. It has one wall at x = L and is very wide in the z direction. When filled with a liquid of surface tension S and density ρ , the liquid surface makes an angle θ_0 ( θ_0 1 ) with the x -axis at x = L . If y(x) is the height of the surface, then the equation for y(x) is:(Take θ(x) ≈ θ(x) ≈ θ(x) = dy/dx and g as acceleration due to gravity) ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/e48999a7-2b29-4d5c-be16-ae2fd5fbcea5.png)

mediumMCQ

A microscope has an objective of focal length 2 cm , eyepiece of focal length 4 cm and the tube length of 40 cm . If the distance of distinct vision of eye is 25 cm , the magnification in the microscope is:

mediumMCQ

An electron (mass 9 × 10^-31 kg and charge 1.6 × 10^-19 C ) moving with speed c/100 ( c = speed of light) is injected into a magnetic field B of magnitude 9 × 10^-4 T perpendicular to its direction of motion. We wish to apply a uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 10^8 ms^-1 ):

mediumMCQ

There are two inclined surfaces of equal length ( L ) and same angle of inclination 45^ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ( μ_k ) between the object and the rough surface is close to:

mediumMCQ

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m . If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the ratio F_A/F_B is:

hardMCQ

A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be ( m is the mass of the electron):

Ready for a Full Test?

Practice with timed mock tests and track your performance across Physics.

Browse Tests Leaderboard

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

Solution & Step-by-step Explanation

Practice this question

Share This Question

Related Questions

Ready for a Full Test?

Discussion