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Q.

The mass of a planet is $1 / 10^{th}$ that of earth and its diameter is half that of earth. The acceleration due to gravity at the planet will be

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a

$9.8 {ms}^{- 2}$

b

$1.96 {ms}^{- 2}$

c

$3.92 {ms}^{- 2}$

d

$19.6 {ms}^{- 2}$

answer is B.

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Detailed Solution

For earth $g = \frac{G M}{R^{2}}$
For planet $g^{'} = \frac{G M^{'}}{R^{' 2}}$
$∴ \frac{g^{'}}{g} = \frac{M^{'}}{M} \times \frac{R^{2}}{R^{' 2}} = \frac{1}{10} \times (2)^{2} = \frac{2}{5}$
Thus $g^{'} = \frac{2 g}{5} = \frac{2}{5} \times 9.8 = 3.92 {ms}^{- 2}$
Hence the correct choice is (2).

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