Two forces, while acting on particle in opposite directions,have the resultant of 10N. If they act at right angles to each other, the resultant is found to be 50N. Find the two forces?

Options

A. `40 N , 30 N`
B. `50 N , 40 N`
C. `30 N , 20 N`
D. `35 N , 25 N`

Answer

A

Explanation

`P - Q = 10` (i)
`P^(2) + Q^(2) = (50)^(2)` (ii)
`(10 + Q)^(2) + Q^(2) = 2500`
`100 + Q^(2) + 20 Q + Q^(2) = 2500`
`Q^(2) + 10 Q - 1200 = 0`
`(Q + 40) (Q - 30) = 0`
`Q = -40 , P = -30`
`Q = 30 , P = 40`
Magnitude of forces : `30 N , 40 N`