Gravitation Tes...

The escape velocity for a planet is $$v_e$$. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its centre. Its speed at the centre of the planet will be

Find the height at which the weight will be same as at the same depth from the surface of the earth.

Use the assumptions of the previous question. An object weighed by a spring balance at the equator gives the same reading as a reading taken at a depth d below the earth's surface at a pole $$(d << R)$$. The value of $$d$$ is

The value of acceleration due to gravity at height $$h$$ from earth surface will become half its value on the surface if (R $$=$$ radius of earth)

Consider a planet moving in an elliptical orbit round the sun. The work done on the planet by the gravitational force of the sun

The gravitational potential difference between the surface of a planet and a point $$20 m$$ above the surface is $$2 Joule/Kg$$. If the gravitational field is uniform then the work done in carrying a $$5 Kg$$ body to a height of $$4 m$$ above the surface is

The magnitude of the potential energy per unit mass of an object at the surface of the earth is given $$U$$. Then, the escape velocity for the object is given by

The value of G for two bodies in vacuum is $$6.67 \times 10^{-11} N-m^2/Kg^2$$. Its value in a dense medium of density $$10^{10} gm/cm^3$$ will be:

The potential energy of a rocket of mass $$100\ kg$$ at height $$10^7\ m$$ from earth surface is $$4 \times 10^9\ Joule$$. The weight of the rocket at height $$10^9$$ will be

A tunnel is dug along a diameter of earth. The force on a particle of mass $$m$$ and distance $$x$$ from the centre in this tunnel will be :