Where will a body weigh more: $1 \, km$ above the surface of the earth or $1 \, km$ below the surface of the earth?

If the diameter of the earth becomes two times its present value and its mass remains unchanged,then how would the weight of an object on the surface of the earth be affected?

If a planet existed whose mass and radius were both half that of the Earth,the acceleration due to gravity at its surface would be: (in $, m s^{-2}$)

When an object, say an apple, falls towards the Earth, the Earth rises up to meet it. Is this true? If so, why is the Earth's motion not noticeable?

$A$ stone is dropped from the edge of a roof. It passes a window $2 \, m$ high in $0.1 \, s$. How far is the roof above the top of the window?

$(a)$ The Earth is acted upon by the gravitation of the Sun,yet it does not fall into the Sun. Why?
$(b)$ An object of mass $500 \, g$ is dropped from a tower of height $5 \, m$. Calculate its momentum when it touches the ground (given $g = 10 \, m s^{-2}$).