An engine pumps water continuously through a hose. Water leaves the hose with a velocity 'v' and mass per unit length is 'm'. What is the power imparted to the water? MCQ with Answer and Explanation

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An engine pumps water continuously through a hose. Water leaves the hose with a velocity 'v' and mass per unit length is 'm'. What is the power imparted to the water?

A. 1/2 m^2v

B. mv^3

C. 1/2 mv^3

D. mv^2

Answer: Option C

Solution (By JKExamLibrary)

Power is the rate of doing work or imparting kinetic energy (dK/dt). Mass exiting per second = m * v (mass/length * length/time). Kinetic energy imparted per second = 1/2 * (mass per second) * v^2 = 1/2 * (mv) * v^2 = 1/2 * m * v^3. This is a very common advanced mechanics question.

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Question #1 Report Error

What is the magnetic dipole moment of an electron revolving in a circular orbit of radius 'r' with a uniform speed 'v'?

A. evr

B. 2evr

C. evr / 2

D. e / (vr)

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Correct Answer: Option C

Explanation:
Magnetic dipole moment M = Current(I) * Area(A). Current is charge/time: I = e / T. Time period T = 2pir / v. So I = ev / (2pir). The area of the circular orbit is A = pir^2. Therefore, M = [ev / (2pir)] * [pir^2] = evr / 2. This is a standard derivation in modern physics.

This question belongs to: Science Physics