If a planet existed, whose mass and radius were both half of that of the earth, what would be the acceleration due to gravity at the surface of the planet in terms of that on the surface of the earth ?

Explanation

Let the gravitional acceleration on the surface of the planet be `g_(p)` and that on the surface of the earth be `g_e`.
Then. `g_(p)/g_(e)=G (M_(p))/R_(p)^(2) divide G (M_(e))/(R_(e)^(2))`
`g_p/g_e=M_p/R_p^2 xx R_e^2/M_e`
Now, `M_p=1/2M_e and R_p=1/2R_e`
`g_p/g_e=(1/2Me)/((1/2 R_e)^(2)) xx R_(e)^(2)/M_e=(1/2)/(1/4)=2`
The gravitional acceleration on tha planet is twice that of on the earth.