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Impulsive Forces in Collision

What will be ...

Question

What will be the acceleration due to gravity at a planet whose mass is eight times the mass of the earth and whose radius is twice that of the earth? ( $g$ on earth is $10 {m s}^{- 2}$ )

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Solution

Acceleration due to gravity = $\frac{G M}{R^{2}}$
For the given planet,
$M$ = $8 M_{e a r t h}$
$R$ = $2 R_{e a r t h}$
Therefore , acceleration due to gravity on the planet = $\frac{G (8 M_{e a r t h})}{(2 R_{e a r t h})^{2}}$
= $2 (\frac{G M_{e a r t h}}{R_{e a r t h}^{2}})$
= $2 g$
= $20$ $m s^{- 2}$

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