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JEE Main & Advanced Physics Vectors Question Bank Addition and Subtraction of Vectors

  • question_answer
    The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are                             [CPMT 1997]

    A)                 6 N and 10 N

    B)                             8 N and 8 N

    C)                 4 N and 12 N      

    D)                 2 N and 14 N

    Correct Answer: A

    Solution :

                        \[A+B=16\] (given)                                          ?(i)                 \[\tan \alpha =\frac{B\sin \theta }{A+B\cos \theta }=\tan 90{}^\circ \]                    \  \[A+B\cos \theta =0\]Þ \[\cos \theta =\frac{-A}{B}\]              ?(ii)                 \[8=\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\cos \theta }\]                              ?(iii)                 By solving eq. (i), (ii) and (iii) we get \[A=6N,\] \[B=10N\]


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