JEE Main & Advanced Physics Vectors Question Bank Topic Test - Vectors

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at \[90{}^\circ \] with the force of smaller magnitude, what are the magnitudes of forces?

A) 12, 5

B) 14, 4

C) 5, 13

D) 10, 8

Correct Answer: C

Solution :

[c] Let p be the smaller force and Q be the greater force then according to problem

\[{{P}_{i}}+Q=18\] ... (i)

\[R=\,\sqrt{{{P}^{2}}+{{Q}^{2}}+\,2PQ\,\,\cos \theta }=12\] ... (ii)

\[\tan \,\phi =\,\frac{Q\,\sin \,\theta }{P+Q\,\cos \theta }\,\,=\,\,\tan \,{{90}^{o}}\,=\infty \]

\[\therefore \] \[P+\,Q\,\,\cos \theta \,=0\] ... (iii)

By solving Eqs. (i), (ii) and (iii) we will get \[P=5\] and \[Q=13\].