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edison (4929)

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Olaaa!! Perrrfect answer. 867  [1164 rates]

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here train is moving in upward direction on an inclined plane having angle of inclination = 30 deg.
acceleration of the train = a = g/2
here component of acceleration in upward direction i.e. normal to the horizontal is (g/2)sin30 and along the horizontal it is (g/2)cos30
let string makes an angle  with the normal to the celing of train.
Tension in the string = T
Resolving the tension along two components as follows:
(a) Vertical to the ground
T cos( - 30) = m[g +(g sin30)/2]     (1)
(b) Along the ground that is in the horizontal direction
T sin( - 30) = mg (cos30)/2     (2)
Dividing eq. (2) by (1) we obtain,
tan( - 30) = [mg (cos30)]/m[g +(g sin30)/2] = 3 /5
or (tan - tan30)/(1+tantan30) = 3 /5
or tan = 2/3
or  = tan-12/
Now to obtain tension in the string square and add then equate LHS and RHS of eq. (1) and (2)
by doing so we obtain and simplifing we obtain
T = 57

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