Gravitation Tes...

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $$V$$. Due to the rotation of planet about its axis the acceleration due to gravity $$g$$ at equator is  $$\dfrac{1}{2}$$ of $$g$$ at poles. The escape velocity of a particle on the pole of planet in terms of  $$V$$.

At what height over the earth's pole does the freefall acceleration decreases by 1% ?

The condition for a uniform spherical mass $$m$$ of radius $$r$$ to be a black hole is [$$G= $$gravitational constant, $$g=$$ acceleration due to gravity].

A body is projected up with a velocity $$2$$ times the escape velocity $$v_{e}$$  from the surface of the earth. The velocity of the body at a point  far away the earth's attraction is

A particle of mass $$10 g$$ is kept on the surface of a uniform sphere of mass $$100 kg$$ and radius $$10 cm$$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere 

The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth d below the surface of the earth.When both $$h$$ and d are much smaller than the radius of earth,then which one of the following is true?

A $$75 kg$$ astronaut is repairing Hubble telescope at a height of $$600 km$$ above the surface of the earth. Find his weight there.

If the orbital speed of moon is increased by $$41.4\%$$ then moon will

A spaceship is released in a circular orbit near the Earth's surface. How much additional velocity will have to be given to the spaceship in order to escape out of this orbit?

Find the work done to take a particle of mass m from surface of the earth to a height equal to $$2R$$.