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NEET Sample Paper NEET Sample Test Paper-67

  • question_answer
    At what angle must the two forces \[\left( x + y \right)\] and \[\left( x - y \right)\] act so that the resultant may be \[\sqrt{\left( {{x}^{2}} + {{y}^{2}} \right)}\]

    A) \[{{\cos }^{-1}}\,\left( -\frac{{{x}^{2}}+{{y}^{2}}}{2({{x}^{2}}-{{y}^{2}})} \right)\]

    B)   \[{{\cos }^{-1}}\,\left( -\frac{2({{x}^{2}}-{{y}^{2}})}{{{x}^{2}}+{{y}^{2}}} \right)\]

    C) \[{{\cos }^{-1}}\,\left( -\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}} \right)\]           

    D) \[{{\cos }^{-1}}\,\left( -\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}} \right)\]

    Correct Answer: A

    Solution :

    \[{{R}^{2}}={{A}^{2}}+{{B}^{2}}+2AB\,\,\cos \,\,\theta \] Substituting, \[A=(x+y),\,\,B=(x-y)\] \[R=\sqrt{({{x}^{2}}+{{y}^{2}})}\] We get \[\theta \,\,=\,{{\cos }^{-1}}\,\left( -\frac{({{x}^{2}}+{{y}^{2}})}{2({{x}^{2}}-{{y}^{2}})} \right)\]


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