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. mv^3
B. 1/2 m^2v
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.
Explanation:
Assertion true: a = -ω²x, max at max |x|. Reason true: F = -kx (Hooke's law), and F = ma ⇒ a ∝ -x. Reason correctly explains why acceleration peaks at extremes. Memory tip: 'SHM: F ∝ -x ⇒ a ∝ -x'. Assertion-reason testing SHM fundamentals, frequently examined in competitive exams.
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