Q 11-04-013NEETJEE MainEAMCET 2012 (Engineering)Easy
The sum of the magnitudes of two forces acting at a point is $16$ N. If their resultant is normal to the smaller force and has a magnitude of $8$ N, then the forces are
Answer: (D) $6$ N and $10$ N
Concept. The resultant is perpendicular to the smaller force, so $F_2$ is the hypotenuse: $F_2^2 - F_1^2 = R^2$.
Step 1. Equations. $(F_2 - F_1)(F_2 + F_1) = 64$, $F_1 + F_2 = 16 \Rightarrow F_2 - F_1 = 4$.
Step 2. Solve. $F_1 = 6$ N, $F_2 = 10$ N.
Answer. $6$ N and $10$ N (Option D).
Solution by Sreeraj P, M.Sc Physics