Question

A planet has twice earth's radius and twice earth's mass. The value of g on this planet would be

Answer 1

Answer:

acceleration due to gravity becomes twice of original. That would be catastrophic for everything on earth hypothetically speaking as the acceleration due to gravity would go up by four times. It will be 4g (4. 9.81 m/s^2 = 39.24 m/s^2).

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Answer 2

The value of g on this planet would be $4.9\ m/s^2$.

Explanation:

The acceleration due to gravity on the surface of Earth is given by the following expression as :

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

For Earth, $g=9.8\ m/s^2$

A planet has twice earth's radius and twice earth's mass, such that,

M' = 2M and R' = 2R

New acceleration due to gravity is given by :

$g'=\dfrac{GM'}{R'^2}$

$g'=\dfrac{G(2M)}{(2R)^2}$

$g'=\dfrac{1}{2}\times \dfrac{G(M)}{(R)^2}$

$g'=\dfrac{1}{2}\times g$

$g'=\dfrac{1}{2}\times 9.8$

$g'=4.9\ m/s^2$

So, the value of g on this planet would be $4.9\ m/s^2$. Hence, this is the required solution.

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