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Question

If F1, F2 makes an angle of 60 and 37 respectively with F3 as shown in the figure, and magnitude of F3 is 2 N, then the magnitude of F1 and F2 respectively are (Given, F1+F2=F3)


A
43(3+4) N and 10(3+4) N
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B
23(3+4) N and 10(3+4) N
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C
43(3+4) N and 5(3+4) N
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D
4(3+4) N and 5(3+4) N
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Solution

The correct option is A 43(3+4) N and 10(3+4) N
Let the magnitude be |F1|=x and |F2|=y
Also, Given, F1+F2=F3
So, the given vectors can be shown as


Now, resolving the vectors along the axes we get
|F3x|=xcos60+ycos37
or, |F3x|=(x2+4y5)
Similarly, |F3y|=xsin60ysin37
or, |F3y|=(3x23y5)


Since, F3 has no component in vertical axis, so, |F3y|=0
(3x23y5)=0
3x2=3y5 x=23y5......(i)
Also, |F3x|=|F3|
(x2+4y5)=2
23y10+4y5=2
y=10(3+4)
and, x=23y5=43(3+4)
Hence, the magnitude of F1 and F2 respectively are 43(3+4) N and 10(3+4) N

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