If the radius of the Earth were to shrink by half while its density remains constant,what would be the weight of an object on the surface of the Earth?

The gravitational pull of the moon is $(1/6)^{\text{th}}$ of the earth and the mass of the moon is $(1/8)^{\text{th}}$ of the earth. This implies that the:

The acceleration due to gravity at an altitude $h$ above the Earth's surface is half of its value on the surface of the Earth. If the radius of the Earth $R = 4000 \ mile$,the altitude $h$ is approximately ......... $mile$.

If the radius of the Earth is $R$,then the height $h$ at which the value of $g$ becomes one-fourth is:

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of the Earth is the same as the acceleration due to gravity at a depth $d = \alpha h$ $(h \ll R_{e})$ from the Earth's surface,then the value of $\alpha$ will be: (use $R_{e} = 6400 \ km$)

If the Earth is assumed to be a sphere of radius $R$,and $g_{30}$ is the value of acceleration due to gravity at a latitude of $30^\circ$ and $g$ is the value at the equator,the value of $g - g_{30}$ is: