NEETPhysicsWork, Power and Energy
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If water is pumped out of a hose pipe of constant cross-sectional area, the mechanical power required is proportional to the square of the ejection velocity. Reason (R): The force required to eject the water stream is proportional to the square of its ejection velocity. In the light of the above st
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
D. (A) is false but (R) is true
Step-by-step solution
For a hose pipe of constant cross-sectional area A , the mass of water ejected per unit time is dm dt = A v , where is the density of water and v is the ejection velocity. The force required to eject the water is equal to the rate of change of momentum of the water stream: F = v dm dt = v( A v) = A v^2 Thus, F v^2 . Therefore, the Reason (R) is true. The mechanical power required by the pump is the product of force and velocity: P = Fv = ( A v^2)v = A v^3 Thus, P v^3 . The Assertion (A) states that power is proport