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JEE Main & Advanced Physics Vectors Question Bank Critical Thinking

  • question_answer
    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° with the force of smaller magnitude, what are the, magnitudes of forces             [Roorkee 1992; AIEEE 2002]

    A)             12, 5                                          

    B)             14, 4

    C)             5, 13                                          

    D)             10, 8

    Correct Answer: C

    Solution :

                           Let P be the smaller force and Q be the greater force then according to problem ?                    P + Q = 18                                                         ......(i)                    \[R=\sqrt{{{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta }=12\]                  .......(ii)                    \[\tan \varphi =\frac{Q\sin \theta }{P+Q\cos \theta }=\tan 90=\infty \]                    \ \[P\text{ }+\text{ }Q\text{ cos}\theta =0\]                                  .......(iii)             By solving (i), (ii) and (iii) we will get \[P=5,\] and \[Q=13\]


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