NEET 2021 Model Test Paper 8

If the motor pumps water (density ρ) continuously through a pipe of area of cross-section A with velocity v, then mass flowing out per second.
m = Avρ ...(i)
Rate of increase of kinetic energy
=

1

2

mv2=

1

2

(Avρ)v2 ...(ii)
Mass m, flowing out per, sec, can be increased to m' by increasing v be v', then power increases from P to P'.

P′

P

=

1 2 Aρv′3

1 2 Aρv3

or

P′

P

=(

v′

v

)3
Now ,

m′

m

=

Av′ρ

Avρ

=

v′

v

As, m′=nm:v′=nv
∴

P′

P

=n3
or P′=n3P.