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