Two forces equal to (F) and ( 3 F) newton act on a particle . If the first force be tripled and the second froce be increased by ` 30` neqton, the disrction of the resultant is unaltaerd. Find the value of (F).

Explanation

Let ` beta` be the angle wich the resultant forec make with the force ` F` and ` theta` be the angle between tow forces.
In first case, ` tan beta = ( 3 F sin theta)/( F+ 3 F cos theta)`
In second case ` : ` tane beta = (( 3 F + 30 ) sin theta)/( 3 F + 30 ) cos theta)` ltbRgt Hence ` ( 3 F sin theta)/( F + 3 F cos theta ) = ( 3 F + 30 ) sin theta)/( 3 F + ( 3 F + 30) cos theta)`
or ` 3 /(1 + 3 cos theta) = ( 3 F+ 30)/( 3 F + F cos theta + 30 cos theta)`
or ` 9 F + 9 F cos theta = 90 cos theta`
`= 3 F + 30 + 9 F cos theta + 90 cos theta`
or ` 9 F- 3 F= 30` or ` F = 5 N`.