If the density of the Earth increases $4$ times and its radius becomes half of its present value,our weight will

How does the acceleration due to gravity $(g)$ at a location on Earth change with latitude?

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (where $x$ and $h$ are much smaller than the radius of the earth $R_e$):

The ratio of the radii of a planet and the earth is $1: 2$, and the ratio of their mean densities is $4: 1$. If the acceleration due to gravity on the surface of the earth is $9.8 \,ms^{-2}$, then the acceleration due to gravity on the surface of the planet is: (in $\,ms^{-2}$)

Obtain the general equation of gravitational force at a distance $r$ from the centre of the Earth and derive the equation for acceleration due to gravity on the surface of the Earth.

If the change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it,then (both $x$ and $h$ being much smaller than the radius of the earth)