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
1 Answer
Sep 22, 2017
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
So we get