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A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = (6.0\times10^{24}) kg; radius of the earth = (6.4 \times 10^{6}) m; G = (6.67 \times 10^{-11} \text{ N m}^{2} \text{ kg}^{-2}).

Two stars each of one solar mass (= (2\times10^{30}) kg) are approaching each other for a head on collision. When they are a distance (10^{9}) km, their speeds are negligible. What is the speed with which they collide ? The radius of each star is (10^{4}) km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable ?

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero ? Mass of the sun = (2\times10^{30}) kg, mass of the earth = (6\times10^{24}) kg. Neglect the effect of other planets etc. (orbital radius = (1.5 \times 10^{11}) m).

How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is (1.5 \times 10^{8}) km.

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is (1.50 \times 10^{8}) km away from the sun ?

A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ?

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

A rocket is fired vertically with a speed of (5 \text{ km s}^{-1}) from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth = (6.0 \times 10^{24}) kg; mean radius of the earth = (6.4 \times 10^{6}) m; G = (6.67 \times 10^{-11} \text{ N m}^{2} \text{ kg}^{-2}).

10.

The escape speed of a projectile on the earth’s surface is (11.2 \text{ km s}^{-1}). A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

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