A gardener waters the plants by a pipe of diameter 1 mm. The water comes out from the pipe atthe rate of 10 cm³/sec. The reactionary force exerted on the hand of the gardener is?

Diameter of pipe = 1 mm

Radius will be, r = 0.5 mm = 0.0005 m

Area of cross-section of the pipe is, A = πr²

Density of water is, d = 1000 kg/m³

Volume of water coming out per sec is = 10 cm³/s = 10^-5 m³/s

Mass of water coming out per sec is,

dm/dt = density × volume/sec

= (1000)(10^-5) kg/s = 10^-2 kg/s

dm/dt = 10^-2 kg/s

Now,

Volume/sec = Area × velocity

A = πr²

 ⁼ 3.14 x (0.0005²)

=> 10^-5 = (3.14) × (0.0005²) × v

=> v = 12.74 m/s

Now, force = change in momentum/sec

=> F = d(mv)/dt

=> F = v(dm/dt) [velocity, ‘v’ is constant]

=> F = (12.74)(10^-2)

=> F = 0.1274 N