NEET Sample Paper NEET Sample Test Paper-39

  • question_answer Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

    A) \[g'=3g\]

    B)  \[g'=\frac{g}{9}\]

    C) \[g'=9g\]

    D) \[g'=27g\]

    Correct Answer: A

    Solution :

     The acceleration due to gravity on the new plan can be found using the relation \[g=\frac{GM}{{{R}^{2}}}\] but \[M=\frac{4}{3}\pi {{R}^{3}}\rho ,\rho \]being density. Thus, Eq. (i) becomes \[\therefore \] \[g=\frac{G\times \frac{4}{3}\pi {{R}^{3}}\rho }{{{R}^{2}}}\] \[=G\times \frac{4}{3}\pi R\rho \] \[\Rightarrow \]\[g\propto R\] \[\therefore \] \[\frac{g'}{g}=\frac{R'}{R}\] \[\Rightarrow \]\[\frac{g'}{g}=\frac{3R}{R}=3\] \[\Rightarrow \]\[g'=3g\]


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