A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun `= 2xx10^30 kg`).

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 107 K, and its outer surface at a temperature of about 6000 K. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases ? Check if your guess is correct from the following data : mass of the Sun = 2.0 xx 10^30 kg , radius of the Sun = 7.0 xx 10^8 m .

The radius of moon is 1.7 xx10^6m and its mass is 7.35xx 10^22 kg . What is the acceleration due to gravity on the surface of moon ? Given G = 6.67 xx 10 ^-11Nm^2//kg^2 .

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s^-1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = 6.4xx10^23 kg , radius of mars = 3395 km, G = 6.67xx10^-11 N m^2 kg^-2 .

The oxygen molecule has a mass of 5.30 xx 10^-26 kg and a moment of inertia of 1.94xx10^-46 kg m^2 about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m//s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

Two stars each of one solar mass (= 2xxl0^30 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).

What is magnitude of gravitational force between the earth and a 1 kg object on its surface ? Take mass of earth to be 6 xx 10^24 kg and radius of the earth is 6.4 xx 10^6 m.G =6.67 xx10^-11nm^2kg^-2 .

Calculate the force of gravitation between the earth and the sun, given the mass of earth = 6xx 10^24 kg and of the sun = 2 xx10^30 kg . Average distance between the two is 1.5xx 10^10m .

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 = 2xxl0^30 kg , mass of the earth = 6xxl0^24 kg . Neglect the effect of other planets etc. (orbital radius = 1.5 xx 10^11 m ).

A rocket is fired vertically with a speed of 5 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 xx 10^24 kg , mean radius of the earth = 6.4 xx 10^6 m , G = 6.67 xx 10^-11 N m^2kg^-2 .