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Question: Two forces of magnitudes F and \(\sqrt{3}\) F act at right angles to each other. Their resultant mak...

Two forces of magnitudes F and 3\sqrt{3} F act at right angles to each other. Their resultant makes an angle b with F. The value of b is –

A

30030^{0}

B

45045^{0}

C

60060^{0}

D

1350135^{0}

Answer

60060^{0}

Explanation

Solution

tan b = Bsin⁡θA+Bcos⁡θ\frac{B\sin\theta}{A + B\cos\theta}

= F3sin⁡θF+F3cos⁡θ\frac{F\sqrt{3}\sin\theta}{F + F\sqrt{3}\cos\theta}

= 3sin⁡θ1+3cos⁡θ\frac{\sqrt{3}\sin\theta}{1 + \sqrt{3}\cos\theta}

tan b = 31\frac{\sqrt{3}}{1} (q = 90090^{0})

β=600\beta = 60^{0}