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Question

If F1, F2 makes an angle of 30 and 45 respectively with F3 as shown in the figure, and magnitude of F3 is 5 N, then the magnitude of F1 and F2 respectively are (Given, F1+F2=F3)


A
52(3+1) N and 5(3+1) N
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B
10(3+1) N and 5(3+1) N
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C
5(3+1) N and 52(3+1) N
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D
10(3+1) N and 52(3+1) N
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Solution

The correct option is D 10(3+1) N and 52(3+1) 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|=xsin30ysin45
or, |F3x|=(x2y2)
Similarly, |F3y|=xcos30+ycos45
or, |F3y|=(3x2+y2)


Since, F3 has no component in horizontal axis, so, |F3x|=0
(x2y2)=0
x2=y2 x=2y......(i)
Also, |F3y|=|F3|
(3x2+y2)=5
3×2y2+y2=5
y=52(3+1)
and, x=2y=10(3+1)
Hence, the magnitude of F1 and F2 respectively are 10(3+1) N and 52(3+1) N

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