Question

Two forces of magnitude 10N and 20N act on a body in directions making angles 30° and 60° respectively with x-axis what is the resultant force
A.17N
B. 19N
C. 23N
D. 29N
E. 37N​

Answer 1

ANSWER:

The resultant force is 29 N.

EXPLANATION:

The resultant of two forces are determined by the parallelogram rule as follows:

As the forces acting at different angle, so the resultant force will have magnitude related to the difference in the angle in which the incident forces were acted.

$\text { Resultant }=\sqrt{F_{1}^{2}+F_{2}^{2}+2 F_{1} F_{2} \cos \left(\theta_{2}-\theta_{1}\right)}$

Here F1 and F2 are the two forces acting and their respective angles are given as   and  

So the resultant force will be

$\text { Resultant force }=\sqrt{(10)^{2}+(20)^{2}+2 *(10 * 20) \cos (60-30)}$

$\text { Resultant force }=\sqrt{100+400+400 \cos (30)}$

$\text { Resultant force }=\sqrt{500+\left(400 * \frac{\sqrt{3}}{2}\right)}$

$\text { Resultant force }=\sqrt{500+(200 * 1.732)}$

$\text { Resultant force }=\sqrt{846.4}$

Thus, the resultant force is 29 N.