Gravitation Tes...

A particle is released from a very large separation from a sphere of mass $$m$$ and radius $$R$$. In which a tunnel is present. Find the ratio of speed acquired by the particle as it reaches the center of the sphere to that of as it reaches its surface. 

In the usual notation, the acceleration due to gravity at a height $$h$$ from the surface of the earth is .........  

The value of the acceleration due to gravity at a height from Earth's surface decreases by $$1\%$$. What will be the value of height from the surface?(Take the radius of earth =$$6400\ km$$)

The change in the value of $$^ { \prime } g ^ { \prime }$$ at a height $$^ { \prime }$$ h'above the surface of the earth is same as at a depth 'd'. If d and h are much smaller than the radius of earth, then which one of the following is correct?

A particle would take a time $$t$$ to move down a straight tube from the surface of earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be $$t$$. The ratio of $$t/t$$ will be

A satellite is revolving around Earth in a circular orbit whose radius is R.work done by gravitational force in one revolution is

Suppose the acceleration due to gravity at the earth's surface is $$10 \mathrm { m } / \mathrm { s } ^ { 2 }$$ and at the surface of mars it is $$4.0 \mathrm { m } / \mathrm { s } ^ { 2 } .$$ A $$60 \mathrm { kg }$$ passenger goes from the earth to the mars in a spaceship moving with a constant velocity. Neglect all other object in the sky. Which part of the figure best represent the weight (net gravitational force) of the passenger as a function of time?

The acceleration due to gravity at a height  $$1 km$$   above the earth is the same as at a depth  $$d$$  below the surface of earth. Then

A man is standing on an international space station, which is orbiting earth at an altitude 520$$\mathrm { km }$$ with a constant speed 7.6 $$\mathrm { km } / \mathrm { s }$$ . If the men's weight is 50$$\mathrm { kg }$$ , his acceleration is

Wt.  of body at height equal to radius of earth