J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    Assuming that the earth is a sphere of radius \[{{R}_{E}}\]with uniform density, the distance from its centre at which the acceleration due to gravity is equal to \[\frac{g}{3}\] (g = the acceleration due to gravity on the surface of earth) is

    A)  \[\frac{{{R}_{E}}}{3}\]            

    B)  \[2\,\,\frac{{{R}_{E}}}{3}\]

    C)  \[\frac{{{R}_{E}}}{3}\]

    D)  \[\frac{{{R}_{E}}}{4}\]

    Correct Answer: B

    Solution :

    Acceleration due to gravity at a depth d is \[g'=g\left[ 1-\frac{d}{{{R}_{E}}} \right]\] \[\Rightarrow \] \[\frac{g}{3}=g\left[ 1-\frac{d}{{{R}_{E}}} \right]\] or \[d=\frac{2}{3}{{R}_{E}}\]


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