The masses of two planets are in the ratio 1:2 their radii are in the ratio 1:2. Find the ratio of the acceleration due to gravity on the planets .

Explanation

Given
Ratio of mass of two plants `=M_1:M_2=1:2`
Ratio of radius of the planet `=R_1:R_2=1:2`
To find : Acceleration due two planets `=g_1:g_2=?`
`g=(GM)/(R^(2))` gravitational Constituent `G=6.674 xx10^(-11) Nm^(2) kg^(-2)`
Solution
`g_1=(GM_1)/(R_1^(2)),g_2=(GM_1)/(2R_1^(2))`
`(g_1)/(g_2)=(GM_1)/(R_1^(2)) xx (2R_2^(2))/(GM_1)=(2)/(1)`
`=(1)/(4) =1:4 ( or ) 1:2`
`g_1:g_2=1:2`