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Question: Two forces of magnitudes 30, 60 and P newton acting at a point are in equilibrium. If the angle betw...

Two forces of magnitudes 30, 60 and P newton acting at a point are in equilibrium. If the angle between the first two is 60°, the value of P is –

A

25225\sqrt{2}

B

30330\sqrt{3}

C

30630\sqrt{6}

D

30730\sqrt{7}

Answer

30730\sqrt{7}

Explanation

Solution

F1→\overset{\rightarrow}{F_{1}}+ F2→\overset{\rightarrow}{F_{2}} + P→\overset{\rightarrow}{P} = 0

∣P→∣|\overset{\rightarrow}{P}| = ∣F1→+F2→∣|\overset{\rightarrow}{F_{1}} + \overset{\rightarrow}{F_{2}}|

= 302+602+2.(30)(60)cos⁡60∘\sqrt{30^{2} + 60^{2} + 2.(30)(60)\cos 60{^\circ}}= 900+3600+1800\sqrt{900 + 3600 + 1800}

= 6300\sqrt{6300}

= 307\sqrt{7} Newton