1. The resultant of two forces F1 and F2 acting at a point is 'R'. If F2 is doubled R is
also doubled and if the direction of F2 is changed R is again doubled. Prove that F1 :
F2: R=√2:√3:√2
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Answer:
See Below
Explanation:
F
2
=F
1
2
+F
2
2
+2F
1
F
2
cosθ
4F
2
=F
1
2
+4F
2
2
+4F
1
F
2
cosθ (Doubling the value of F
2
)
4F
2
=F
1
2
+F
2
2
−2F
1
F
2
cosθ (Reversing the direction of F
2
)
Solving the above equations, we get, F
2
2
=F
2
and F
1
2
=
2
3
F
2
Then F
1
:F
2
:F
3
=
3
:
2
:
2
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