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?

give proper answer​

Answer 1

Answer:

Let the other Force be of magnitude x and the angle it makes with resultant be θ.

Now, the components of the two vectors along the resultant should be of magnitude of the resultant and the component of these two vectors resolved in the direction perpendicular to resultant should be zero.

In other words, 20  

3

​  

cos30  

0

+xcosθ=20

which gives, 20  

3

​  

.  

2

3

​  

 

​  

+xcosθ=20

or, 30+xcosθ=20, giving xcosθ=−10 --- (1)

Now, resolving in the perpendicular direction, 20  

3

​  

.sin30  

0

+xsinθ=0

or, 10  

3

​  

+xsinθ=0, giving xsinθ=−10  

3

​  

 --- (2)

Squaring and adding (1) and (2), we get:

(xcosθ)  

2

+(xsinθ)  

2

=x  

2

=100+300=400 , thus x=20 N

Explanation: