Question

X and Y are planets.Accelaration due to gravity at a height half the radius from surface of planet X is equal to that of at the surface of planet Y. If mass of X is four times that of Y, ratio of radii of planets X and Y is ? A) 4:3 B) 3:4 C) 2:1 D) 1:2

Answer 1

Let

• Mass and radius of planet X are `M_x and R_x` respectively

• Mass and radius of planet Y are `M_y and R_y` respectively

• .Acceleration due to gravity at a height half the radius from surface of planet X

`g_x=(GM_x)/(R_x+R_x/2)^2=(GM_x)/(9/4R_x^2)`

• .And acceleration due to gravity at the surface of planet Y

`g_y=(GM_y)/R_y^2` , where G is gravitational constant

Again `M_x=4M_y and g_x=g_y`

So we get

`(GM_x)/(9/4R_x^2)=(GM_y)/R_y^2`

`=>(G4M_y)/(9/4R_x^2)=(GM_y)/R_y^2`

`=>R_x^2/R_y^2=16/9`

`=>R_x/R_y=4/3`