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
gx=Mx/rx^2
gy=My/ry^2
but mass=k*4/3 PI r^3
so if k for each planet is the same..
gx=k (4/3 PI rx^3) and
gy=k (4/3 pi ry^3)
gx/gy=(.5rx/ry)^3=1 or rx/ry=cubrt8=2
rx=2ry or rx/ry=2/1