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Question: The resultant of two forces has magnitude 20 N. One of the forces is of magnitude \(20\sqrt{3}\)N an...

The resultant of two forces has magnitude 20 N. One of the forces is of magnitude 20320\sqrt{3}N and makes an angle of 30ŗ with the resultant. Then, the other force must be of magnitude -

A

10 N

B

10310\sqrt{3} N

C

20 N

D

20320\sqrt{3} N

Answer

20 N

Explanation

Solution

R→=A→+B→\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B}

B→=R→−A→\overrightarrow{B} = \overrightarrow{R} - \overrightarrow{A}

∣B→∣|\overrightarrow{B}| = R2+A2−2RAcos⁡θ\sqrt{R^{2} + A^{2} - 2RA\cos\theta}

= (20)2+(203)2−2×20×203cos⁡30º\sqrt{(20)^{2} + (20\sqrt{3})^{2} - 2 \times 20 \times 20\sqrt{3}\cos 30º}