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Question

The greatest and the least resultant of two forces acting at a point are 10 N and 6 N, respectively. If each force is increased by 3 N and are acting at a point making an angle of 90o with each other. Find the resultant of new forces.

A
146 N
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B
124 N
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C
188 N
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D
114 N
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Solution

The correct option is A 146 N
Let a,b be two vectors of magnitudes a,b
Given,
a+b=10
ab=6
Adding the equations 2a=16
a=8,b=2
Now magnitude of each vector is increased by 3 N
a1=a+3=11 N
b1=b+3=5 N
Given that new vectors act at 90o, so resultant is
R=a21+b21+2a1b1cos90o
R=112+52=146 N

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