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Question

Two forces acting on a particle in opposite directions have a resultant of 10 kg wt. If they act at right angles to each other, the resultant is 60kg wt. The forces are (in kg. wt):

A
47.4, 37.4
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B
14.3, 24.3
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C
40, 30
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D
60, 70
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Solution

The correct option is A 47.4, 37.4
When forces are in opposite direction the net magnitude is 10.
Let the forces be x and 10+x.
When they act in 90 degrees, the net magnitude is 60
Therefore,
60=x2+(10+x)2
3600=2x2+100+20x
2x2+20x3500=0
x2+10x1750=0
Solving the quadratic equation gives x=37.4 or x=47.4 but since magnitude is always positive x=37.4 and the other force is 47.4.

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