Gravitation Tes...

If $$g$$ is the acceleration due to gravity on the earth's surface, the gain of the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth will be :

Calculate angular velocity of earth so that acceleration due to gravity at $$60^o$$ latitude becomes zero. (Radius of earth $$=6400$$km, gravitational acceleration at poles$$=10m{/s^2}, \cos 60^o=0.5$$)

Assuming $${ g }_{ \left( moon \right)  }=\left( \dfrac { 1 }{ 6 }  \right) { g }_{ earth }$$ and $${ D }_{ \left( moon \right)  }=\left( \dfrac { 1 }{ 4 }  \right) { D }_{ earth }$$ where $$g$$ and $$D$$ are the acceleration due to gravity and diameter respectively, the escape velocity from the moon is:

Weight of a body of mass m decreases by $$1 \%$$ when it is raised to height $$h$$ above the earth's surface. If the body is taken to a depth $$h$$ in a mine, change in its weight is:

How far above the earth's surface must an astronaut in space be if they are to feel a gravitational acceleration that is half what they would feel on the surface of the earth?

Calculate the value of $$g$$ on the surface of planet if the planet has $$1/500$$ the mass and $$1/15$$ the radius of the Earth.

An astronaut who weighs $$162$$ pounds on the surface of the earth is orbiting the earth at a height above the surface of the earth of two earth radii ($$h = 2R$$ where R is the radius of the earth.)
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)

A person normally weighs 800N at sea level, climbs to the top of a mountain. While on top of the mountain that person will weigh:

Calculate the mass and weight of the object which is at height of twice the radius of the Earth from the surface of the Earth, if mass and weight of the object is $$m$$ and $$w$$ respectively.

Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object A) so that only its gravitational potential energy changes.
How many times does the height of object B change compared to the height change of object A, as result of the work done?