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

  • 54

tough to explain, bro

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