Gravitation Tes...

Consider a satellite moving in a circular orbit around Earth. If K and V denote its kinetic energy and potential energy respectively, then(Choose the convention, where $$V=0$$ as $$r\rightarrow \infty$$)

A body of mass $$m$$ is raised from the earths, surface to an altitude equal to the radius (R) of the Earth. If $$g$$ is the gravitational acceleration on the Earth's surface

Weight of a body at the equator of a planet is half of that at the poles. If peripheral velocity of a point on the equator of this planet is $$ v_0 $$, what is the escape velocity of a polar particle? 

Find the changes is gravitational potential energy if a particle of mass $$2\ kg$$ is taken from the origin to the point $$(12\ m, 5\ m)$$

Find the change in potential energy if the particle is taken from $$(12\ m,0)$$ to $$(0,5\ m)$$

The value of G is

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine $$100 \ km$$ below the earth's surface (Given $$R= 6400 \ km$$)

Acceleration due to gravity is '$$g$$' on the surface of the earth. The value of acceleration due to gravity at a height of $$32 \ km$$ above earth's surface is (Radius of the earth $$=6400 \ km$$)

At the center of the earth:

At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface ( R = radius of earth)