Question

1. The resultant of two forces F1 and F2 acting at a point is 'R'. If F2 is doubled R is
also doubled and if the direction of F2 is changed R is again doubled. Prove that F1 :
F2: R=√2:√3:√2​

Answer 1

Answer:

See Below

Explanation:

F  

2

=F  

1

2

​  

+F  

2

2

​  

+2F  

1

​  

F  

2

​  

cosθ

4F  

2

=F  

1

2

​  

+4F  

2

2

​  

+4F  

1

​  

F  

2

​  

cosθ (Doubling the value of F  

2

​  

)

4F  

2

=F  

1

2

​  

+F  

2

2

​  

−2F  

1

​  

F  

2

​  

cosθ (Reversing the direction of F  

2

​  

)

Solving the above equations, we get, F  

2

2

​  

=F  

2

 and F  

1

2

​  

=  

2

3

​  

F  

2

 

Then F  

1

​  

:F  

2

​  

:F  

3

​  

=  

3

​  

:  

2

​  

:  

2

​