Question

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain thrice as much water from the same pipe in the same time, power of the motor has to be increased to:

• A. $3$ times
• B. $9$ times
• C. $27$ times
• D. $81$ times

Answer 1

Answer: (C)

$27$ times

Power is the rate at which energy is consumed hence,

$P=\frac{E}{t}$

$P=\frac{\frac{1}{2}m{v}^2}{t}$

Hence, from above equation power of motor to deliver thrice as much water from the same pipe in the same time, will be

velocity will also become trice because we want trice time water than the previous case from the same pipe

$P^{\prime }=\frac{\frac{1}{2}\left(3\right)m(3v{)}^2}{t}$

$P^{\prime }=3\left[\frac{\frac{1}{2}m(3v{)}^2}{t}\right]$

$P^{\prime }=27P$