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

Answer:

$g_{planet} = \frac{3}{2}g$

Explanation:

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

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

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

so we will have

$M = \rho \times \frac{4}{3}\pi R^3$

Now we have

$g = \frac{G(\rho \frac{4}{3}\pi R^3)}{R^2}$

$g = \frac{4}{3}\rho \pi R G$

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

$g_{planet} = \frac{4}{3}(3\rho)\pi (\frac{R}{2}) G$

$g_{planet} = \frac{3}{2}g$