Q95 / 270 · NDA 2018 (Phase 2) · General Ability

A planet has a mass $M_1$ and radius $R_1$. The value of acceleration due to gravity on its surface is $g_1$. There is another planet 2 , whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2 ?

  • A
    $\mathrm{g}_1$
  • B
    $2 \mathrm{~g}_1$
  • Correct answer
    C
    $\mathrm{g}_1 / 2$
  • D
    $\mathrm{g}_1 / 4$

Solution

The acceleration experienced by the mass $\mathrm{M}_1$, on planet 1 is given by $\mathrm{g}_1=\mathrm{GM}_1 / \mathrm{R}_1^2$, similarly the $\mathrm{g}_2=\mathrm{G}_2 \mathrm{M}_1 / 4 \mathrm{R}_1{ }^2$, hence, $\mathrm{g}_1 / \mathrm{g}_2=2 / 1$ or $\mathrm{g}_2=\mathrm{g}_1 / 2$

Hence, the correct answer is option: 'C'.

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