A motor of power `P_0` is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the moter is increased to `P_1` to `P_0` is

Options

A. n-times
B. `n^(2)-times`
C. `n^(3)-times`
D. `n^(4)-times`

Answer

c

Explanation

Mass flowing out per second, m=Avp
`K.E1/2mv^(2)=1/2(Avp)V^(2)`
if the mass, velocity and power of moter in crease from m to m1vto v1 and p to p1 respectively, then
` p/p=(1/2APv1^(3))/(1/2ApV^(3))=m1/m=(v1)^(3)/v^(3)`
`m_(1)-=nm,v_(1)=nV`
` p1/p=n^(2)`
` p_(1)=n^(3)P`