A pump motor is used to deliver water at a certain rate from a given pipe. To obtain 'n' times water from the same pipe in the same time, by what amount the power of the motor should be increased?

Options

A. `n^2` times
B. `n^3` times
C. `n` times
D. `n^(3//2)` times

Answer

B

Explanation

If the motor pumps water `(density = rho)` Continously througha pipe of area of cross sector A with velocity `v`, then mass following out per second , `m = Av rho` Rate of increase of kinetic energy = Power of pump:
`P = (1)/(2)mv^(2) = (1)/(2) (Av rho)v^(2) = (1)/(2) (Av rho)v^(3)`
To get double amount of water , velocity should be double . Hence power becomes `8` times.