Consider a planet in some solar system which has a mass double

[draotic]

Homework Statement

Consider a planet in some solar system which has a mass double the mass of Earth and same density as of Earth . What is the weight of object on the planet in terms of 'W' , where 'W' is weight of object on Earth

Homework Equations

W=mg ... density = M / V . ... g=GM/R²

The Attempt at a Solution

since they both have same density..
i equated their M/V ratios and it gets me the ratio of their radii ..
but it still gets me nowhere

 

[Pengwuino]

Letting 'D' indicate the information you know for the double sized planet, you know

[itex]M_{D} = 2M_{Earth}[/itex]

and you know [itex]R_{D} = X R_{Earth}[/itex] where X is whatever you determined the ratio between the radii are. So simply find what the gravitational acceleration on this new planet will be with [itex]g = {{GM}\over{R^2}}[/itex]. The trick will be being able to write 'g' as [itex]g = Y \times {{GM_{Earth}}\over{R_{Earth}^2}}[/itex] where you have some constant, 'Y', multiplying the original values known for the Earth. Those known values you know gives [itex]g_{Earth} = 9.8 m/s[/itex].

You'll have some multiplicative value in front that will tell you how many times stronger or weaker the gravity is.

 

[draotic]

Letting 'D' indicate the information you know for the double sized planet, you know

[itex]M_{D} = 2M_{Earth}[/itex]

and you know [itex]R_{D} = X R_{Earth}[/itex] where X is whatever you determined the ratio between the radii are. So simply find what the gravitational acceleration on this new planet will be with [itex]g = {{GM}\over{R^2}}[/itex]. The trick will be being able to write 'g' as [itex]g = Y \times {{GM_{Earth}}\over{R_{Earth}^2}}[/itex] where you have some constant, 'Y', multiplying the original values known for the Earth. Those known values you know gives [itex]g_{Earth} = 9.8 m/s[/itex].

You'll have some multiplicative value in front that will tell you how many times stronger or weaker the gravity is.

thanks , got it