Gravitation Tes...

The dependence of acceleration due to gravity $$g$$ on the distance $$r $$ from the centre of the earth, assumed to be a sphere of radius $$R$$ of uniform density is as shown in figures below. The correct figure is

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:

If $${v}_{e}$$ is escape velocity and $${v}_{o}$$ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by :

A particle of mass $$m$$ is thrown upwards from the surface of the earth, with a velocity $$u$$. The mass and the radius of the earth are, respectively, $$M$$ and $$R$$. $$G$$ is gravitational constant and $$g$$ is acceleration due to gravity on the surface of the earth. The minimum value of $$u$$ so that the particle does not return back to earth is

Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by which of the following options ?

A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

The change in the gravitational potential energy when a body of mass $$m$$ is raised to a height $$nR$$ above the surface of the earth is (here $$R$$ is the radius of the earth).

The value of $$g$$ at a height of $$100km$$ from the surface of the Earth is nearly (Radius of the Earth $$=$$ 6400km) ($$g$$ on the surface of the Earth $$=$$ $$9.8m/s^{2}$$)

The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ km/s. If the body is projected at an angle of $$45^{0}$$ with the vertical, the escape velocity will be

If $$g$$ on the surface of the Earth is $$9.8\  ms^{-2}$$, its value at a height of $$6400 km$$ is: (Radius of the Earth $$= 6400km$$)