Question

The resultant of two forces has magnitude 20 N. One of
the forces is of magnitude 20/3 N and makes an angle
of 30° with the resultant. Then what is the magnitude of
the other force?​

Answer 1

Answer

• Magnitude of other force is 20 N

Given

• The resultant of two forces has magnitude 20 N
• One of  the forces is of magnitude 20√3 N
• And makes an angle  of 30° with the resultant

To Find

• Magnitude of other force

Formula Used

$\bf \bigstar \;\; \vec{A}+\vec{B}=\vec{R}$

Solution

A = 20 N ,

B = ? N ,

R = 20√3 N ,

θ = 30°

$\implies \rm \vec{A}+\vec{B}=\vec{R}\\\\\implies \rm \vec{B}=\vec{R}-\vec{A}\\\\\implies \rm B^2=R^2+A^2-2RA\cos \theta\\\\\implies \rm B^2=(20\sqrt{3})^2+(20)^2-2(20\sqrt{3})(20)\cos(30)\\\\\implies \rm B^2=400 \times 3+400-800\sqrt{3}\bigg(\dfrac{\sqrt{3}}{2}\bigg)\\\\\implies \rm B^2=1200+400-400\times 3\\\\\implies \rm B^2=1600-1200\\\\\implies \rm B^2=400\\\\\implies \rm B^2=(20)^2\\\\\implies \rm B=20\ N$

So , magnitude of the other force , B = 20 N