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NEET Sample Paper NEET Sample Test Paper-37

  • question_answer
    A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to \[\upsilon (x)=\beta {{x}^{-2n}}\] where\[\beta \]and\[n\]are constants and x is the position of the particle. The acceleration of the particle as a function of \[x\]is given by

    A) \[-2n{{\beta }^{2}}{{x}^{-2n-1}}\]

    B) \[-2n{{\beta }^{2}}{{x}^{-4n-1}}\]

    C) \[-2n{{\beta }^{2}}{{x}^{-2n+1}}\]

    D) \[-2n{{\beta }^{2}}{{e}^{-4n+1}}\]  

    Correct Answer: B

    Solution :

     We are given velocity of the particle \[\upsilon (x)=\beta {{x}^{-2n}}\] We know acceleration\[a=\upsilon \frac{d\upsilon }{dx}\] \[a=\beta {{x}^{-2n}}\frac{d}{dx}(\beta {{x}^{-2n}})\] \[={{\beta }^{2}}{{x}^{-2n}}(-2n){{x}^{-2n-1}}=-2n{{\beta }^{2}}{{x}^{-2n-1-2n}}\] \[a=-2n{{\beta }^{2}}{{x}^{-4n-1}}\]


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