JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    If g be the acceleration due to gravity and K be the rotational kinetic energy of the earth. If the earth's radius increases by 2% keeping mass constant, then

    A)  Both decrease by 4%                         

    B)  g decrease by 4% and K decrease by 2%

    C)  Both decrease by 2%                         

    D)  g decrease by 4% and K increase by 4%

    Correct Answer: A

    Solution :

     Acceleration due to gravity is\[g=\frac{GM}{{{R}^{2}}}\] and if L be the angular momentum of the earth, then rotational\[KE=\frac{{{L}^{2}}}{2l}\], where l be the moment of inertia. So,   \[l=\frac{2}{5}M{{R}^{2}}\] (for sphere) \[\therefore \] Rotational KE = \[\frac{5{{L}^{2}}}{4M{{R}^{2}}}\] Since, angular momentum remains conserved. So,  rotational KE \[(K)\propto \frac{1}{{{R}^{2}}}\] \[\therefore \] Both g and K are\[\propto {{R}^{-2}}\]. \[\therefore \]\[\frac{\Delta g}{g}=\frac{\Delta K}{K}=-2\times \frac{\Delta R}{R}\] \[\therefore \]Both g and K would decrease by\[2\times 2%=4%\]

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