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
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 JKSSB Mock Tests)
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.
According to Kepler's Third Law of Planetary Motion, the square of the time period of revolution of a planet around the Sun is directly proportional to:
A.The mass of the planet
B.The square of the semi-major axis of its elliptical orbit
C.The cube of the mass of the Sun
D.The cube of the semi-major axis of its elliptical orbit
Explanation:
Kepler's Third Law (Law of Periods) states that the square of the time period (T^2) of any planet is proportional to the cube of the semi-major axis (r^3) of its orbit. Mathematically, T^2 is proportional to r^3. This law helps in calculating orbital periods or distances of planets and satellites.
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