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BCECE Engineering BCECE Engineering Solved Paper-2014

  • question_answer
    The gravitational, field due to a mass distribution is \[E=\frac{k}{{{x}^{3}}}\] in the \[x\] - direction, where k is a constant. The value of gravitational potential at a distance \[x\] is [Taking gravitational potential to be zero at infinity]

    A) \[\frac{k}{x}\]                                   

    B) \[\frac{k}{{{x}^{3}}}\]

    C) \[\frac{k}{2{{x}^{2}}}\] 

    D) \[\frac{k}{3{{x}^{3}}}\]

    Correct Answer: C

    Solution :

    Gravitational potential \[=\int_{{}}^{{}}{ldx}\] Given,     \[l=E=\frac{k}{{{x}^{3}}}\] \[\therefore \]  \[\int_{x}^{\infty }{\frac{k}{{{x}^{3}}}dx}\] \[=k\left[ \frac{{{x}^{-3+1}}}{-3+1} \right]_{x}^{\infty }=k\left[ \frac{-1}{2{{x}^{2}}} \right]_{x}^{\infty }=\frac{k}{2{{x}^{2}}}\]                                


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