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

Two forces of magnitude 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 = 3Fsin⁡90ºF+3Fcos⁡90º\frac{\sqrt{3}F\sin 90º}{F + \sqrt{3}F\cos 90º}

= 3FF\frac{\sqrt{3}F}{F} = 3\sqrt{3}

β=600\beta = 60^{0}