Tow forces `F and 2 F` newton act on a paricle. If the first force be doubled and the secon force be increased by `20 N`, the direction of resultant is unaltered. Find the value of bigger force.

Explanation

Let ` theta` be the angle between two forces `F and 2 F and beta` be the anle which the resultant force makes with the force (F).
` In first case, tan beta =(2 f sin theta) /(F + 2 F soc theta)`
In second case, tan beta =((2 F + 20) sin theta ) /(2 F + (2 F + 20 ) cos theta)`
Hence, `(2 F sin theta)/(F + 2 F cos theta ) =( (2 F + 20 ) sin theta)/(2 F + (2 F + 20 )cos theta)`
[As , A/B =C/D =(C-A)/ (D-B)]`
so ` ( 2F sin theta ) (F + 2F cos theta) `
`=((2 F + 20 20 0sin theta -2 F sin theta) (2 F + (2 F + 20 ) cos theta -(F = 2F cos theta))`
`= 920sin theta) /(F + 20 cos theta)`
Form above we have, ` 2 F =20 or F = 10 N`
Bigger force `=2 F xx10 20 N`.