Question

If the radius of a planet is twice the earth, the value of g will be __ times that of earth​

Answer 1

Answer:

2.45 m/s

Explanation:

For instance, if an object were moved to a location that is two earth-radii from the center of the earth - that is, two times 6.38x106 m - then a significantly different value of g will be found. As shown below, at twice the distance from the center of the earth, the value of g becomes 2.45 m/s2.

Answer 2

Let, g be the g gravity of the Earth,

and g' be the gravity of the planet

$g = \frac{GM}{ {r}^{2} } \: \: \: \: \: .... (i) \\ \\ g' = \frac{GM}{ {(2r)}^{2} } \: \: \: \: \: ....(i)\\ \\ \frac{g}{g'} = \frac{ \frac{GM}{ {r}^{2} } }{ \frac{GM}{4 {r}^{2} } } \\ \\ \\ \frac{g}{g'} = \frac{ \cancel{GM}}{ \cancel{{r}^{2} }} \times \frac{4 \cancel{{r}^{2}} }{ \cancel{GM} } \\ \\ \frac{g}{g'} = 4 \\ \\ g' = \frac{g}{4}$

So, the gravity of planet will be 1/4 times the value of g of the earth.