Question

A gardener waters plants by a pipe of cross section 1mm^2.the water comes out at the rate of 100cc/sec.the reactionary force exerted on the hand of the gardener is----? iknow the answer....just tell me the steps not the answer...​

Answer 1

given, cross sectional area of pipe , A = 1mm² = 10^-6 m²

water comes out at the rate 100cc/s or 100cm³/sec.

so, volume of water comes out in a second , V = 100cm³ = 100 (10^-2)³ m³

= 10^-4 m³

we know, density of water , ρ = 1000 kg/m³

so, mass of water comes out in a second = ρV = 1000 × 10^-4 = 0.1 kg

so, mass of water comes out in ∆t seconds , m = (0.1∆t)Kg

now, find velocity of water flows , v = rate of flow of water/cross sectional area of pipe = V/A = (10^-4)/(10^-6) = 100 m/s

from Newton's 2nd law,

force = rate of change of momentum with respect to time.

or, F = ∆p/∆t

= (mv)/∆t

= (0.1∆t)(100)/∆t

= 10 N

hence, reactionary force exerted on the hand of the gardener is 10N.