Question

15. A gardener waters plants by a pipe of cross
section 1 mm2. The water comes out at the rate
of 100 cc/s. The reactionary force exerted on the
hand of the gardener is
(1) 10 N
(2) 100 N
(3) 1000 N
(4) 500 N

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Answer 1

answer : option (1) 10N

explanation : 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.

Answer 2

See the attachment

The correct answer is 10 N