Question

A wide hose pipe is held horizontally by a fireman, it delivers water through a nozzle at one litre per second. On increasing the pressure, this increases to two litres per second. Now the fireman has to

• A. push forward twice as hard
• B. push forward four times as hard
• C. push backward four times as hard
• D. push backward twice as hard

Answer 1

The correct option is B push forward four times as hard

We know mass is the product of volume and density

$m=\rho v$

as the volume increased then new mass is

$m=\rho \times 2v=2\rho v$

and velocity also doubled from $1litre/second$ to $2litre/second$

Force is rate of change of momentum

$F=ma=m\times \frac{v}{t}=\frac{mv}{t}$

new force $F^{{}^{\prime }}$ is $F^{{}^{\prime }}=2m\times \frac{2v}{t}=\frac{4mv}{t}=4F$

now the man has to push forward $4$ times.