Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .

Two forces equal to P and 2P newton act on a particle . If the first b

1.	Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .
Answer» <P> Solution :Let the resultant make angle `beta`with the force P . `:.`In FIRST case, `tan beta = (2 P sin theta)/( P + 2 P cos theta)` In second case, `tan beta = ((2P + 20) sin theta)/(2P + (2P + 20) cos theta)` HENCE, `((2P + 20) sin theta)/( 2 P + (2P + 20) cos theta) = (2P sin theta)/(P + 2 P cos theta)` (or)`(2P sin theta)/( P +2 P cos theta) = (2 0 sin theta)/( P + 2 0 cos theta)`[`:' (a)/(b) = (c)/(d) = (a-c)/(b-d)` ] From the above EQUATION , 2P = 20 (or) P = 10 N