80 railway wagons all of same mass 5*103 are pulled by a force 4*105 N . the tension in coupling between the 30 and the 31 wagon from the engine is

( ans= 25*104 N)

From Newton's second law,
F=ma
or 4x105 =80 x 5000 x a
a=1 m/s2
Tension developed in the coupling between 30th and 31st wagon will be due to the mass of remaining 50 wagons.
Now mass of the remaining 50 wagons=50 x 5000=250000 kg
Hence required tension=250000 x 1=250000  N=25 x 104 N

  • 51

Aceleration of the wagons = a

Force = total mass x acceleration

a = 4*105 / 80 x 5 x 103 = 4*105 / 4*105 = 1 m/s2

--

Number of wagons from 31 to 80 = 50

Mass of 50 wagons = 50 X 5*103 = 25*104 kg

acceleration of 50 wagons = 1m/s2

--

Tension between 30-31 coupling = force required to produce an acceleration of 1 ms-2 in 50 wagons

T = 25*104 kg x 1 ms-2 = 25 x 104 N

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