Question

Planet X has the half the size of Earth and a density three times that of the Earth. Determine the acceleration due to gravity on Planetx Select one: 9/2 2g/3 39/2 2g 3

Answer 1

`g_(planet) = (3)/(2)g`

Step-by-step explanation:

As we know that the acceleration due to gravity is given as

`g = (GM)/(R^2)`

now we know that mass is the product of density and volume

so we will have

`M = \rho * (4)/(3)\pi R^3`

Now we have

`g = (G(\rho (4)/(3)\pi R^3))/(R^2)`

`g = (4)/(3)\rho \pi R G`

now size of new planet is half that of size of Earth and the density is 3 times the density of Earth

so we have

`g_(planet) = (4)/(3)(3\rho)\pi ((R)/(2)) G`

`g_(planet) = (3)/(2)g`