Question

engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass

per unit length of the water jet. What is the rate at which kinetic energy is imparted water?

[AIPMT (Prelims)-2009]​

Answer 1

answer : 1/2 mv³

explanation : engine pumps water continuously through a hose. water leaves the hose with the velocity v and m is mass per unit length of water jet.

let l length of water is passed during time t.

so, total mass of water = ml

and mass of water per second = ml/t

= m(l/t) = mv [ as we know, velocity = displacement/time so, v = l/t ]

now, kinetic energy per second = 1/2 × mass of water per second × v²

= 1/2 (mv)v²

= 1/2 mv³

hence, rate of kinetic energy at which it is imparted water = 1/2 mv³

Answer 2

Answer:

1/2mv³

Explanation:

Given,

Mass per unit length =m

So total mass of water =m*l=ml

So,

Kinetic energy of water =1/2*ml*v²

And rate of kinetic energy imparted to water =(K.E./t) =(1/2*m*l*v²)/t

=1/2* m* (l/t) *v²

=1/2*m*v*v²

=1/2*m*v³

=1/2mv³