Q131 / 200 · NEET 2024 · Physics

The mass of a planet is $\frac{1}{10}$ th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

  • A
    $9.8 \mathrm{~m} \mathrm{~s}^{-2}$
  • B
    $4.9 \mathrm{~m} \mathrm{~s}^{-2}$
  • Correct answer
    C
    $3.92 \mathrm{~m} \mathrm{~s}^{-2}$
  • D
    $19.6 \mathrm{~m} \mathrm{~s}^{-2}$

Solution

$\begin{aligned} g^{\prime}=\frac{G M^{\prime}}{R^2} & =\frac{G M}{10\left(\frac{R}{2}\right)^2} \\ & =\frac{4}{10} \frac{G M}{R^2}=0.4 \times 9.8 \\ & =3.92 \mathrm{~m} \mathrm{~s}^{-2}\end{aligned}$

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

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