The sum of magnitudes of two forces acting at a point is 16N. If their resultant is normal to the smaller force and has a magnitude of 8N. Then the forces are

The sum of magnitudes of two forces acting at a point is 16N. If their

1.	The sum of magnitudes of two forces acting at a point is 16N. If their resultant is normal to the smaller force and has a magnitude of 8N. Then the forces are
Answer» Solution :Let `vecF` be the resultant of TWO forces `vecF_(1) and vecF_(2)` as SHOWN in figure with `F_(2)>F_(1)`. `F_(2)SINTHETA = F_(1)""……..(i)` `F_(2)costheta= F = 8 ""…………(ii)` Squarting and adding Eqs (i) and (ii), we get `F_(2)^(2) = F_(1)^(2) + 64"".........(iii)` Given `F_(1)+F_(2) = 16""............(iv)` Solving Eqs. (iii) and (iv), we get `F_(1) = 6N and F_(2) = 10N`