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