If the mass of earth is 80 times that of moon and diameter is double that of moon and g on the surface of earth is9.8 ms−2 . Then the value of g on the moon is

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If the mass of earth is 80 times that of moon and diameter is double that of moon and g on the surface of earth is $9.8 {ms}^{- 2}$ . Then the value of g on the moon is

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0.98 {ms}^{- 2}

4.9 {ms}^{- 2}

49 {ms}^{- 2}

0.49 {ms}^{- 2}

answer is A.

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Detailed Solution

M_{e} = 80 M_{m}

$D_{e} = 2 D_{m}$

$\Rightarrow R_{e} = 2 R_{m}$

$g = \frac{GM}{R^{2}}$

$\Rightarrow \frac{g_{m}}{g_{e}} = \frac{M_{m}}{M_{e}} {(\frac{R_{e}}{R_{m}})}^{2}$

$= \frac{g_{m}}{g_{e}} = \frac{M_{e}}{M_{e}} {(\frac{R_{e}}{R_{m}})}^{2}$

$= \frac{1}{80} {(2)}^{2}$

$= \frac{1}{20}$

$\Rightarrow g_{m} = \frac{9.8}{20} = 0.49 {ms}^{- 2}$

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