If F1, F2 makes an angle of 30∘ and 45∘ respectively with F3 as shown in the figure, and magnitude of F3 is 5N, then the magnitude of F1 and F2 respectively are (Given, −→F1+−→F2=−→F3)
A
5√2(√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 5√2(√3+1)N
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D
10(√3+1)N and 5√2(√3+1)N
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Solution
The correct option is D10(√3+1)N and 5√2(√3+1)N Let the magnitude be |−→F1|=xand|−→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|=xsin30∘−ysin45∘ or, |−−→F3x|=(x2−y√2) Similarly, |−→F3y|=xcos30∘+ycos45∘ or, |−→F3y|=(√3x2+y√2)
Since, −→F3 has no component in horizontal axis, so, |−−→F3x|=0 ⇒(x2−y√2)=0 ⇒x2=y√2⇒x=√2y......(i) Also, |−→F3y|=|−→F3| ⇒(√3x2+y√2)=5 ⇒√3×√2y2+y√2=5 ⇒y=5√2(√3+1) and, ⇒x=√2y=10(√3+1) Hence, the magnitude of F1 and F2 respectively are 10(√3+1)N and 5√2(√3+1)N