Problems Based on Universal Law of Gravitation

Q.1. If the distance between two masses is increased by a factor of 4, by what factor would the mass of one of them have to be altered to maintain the same gravitational force?

Q.2. The gravitational force between two objects is F. How will this force change when (i) distance between them is reduced to half (ii) the mass of each object is quadrupled?

Q.3. A geostationary satellite is orbiting the earth at a height 5 R above the surface of earth, where R is the radius of earth. Find the time period of another satellite at a height of 2 R from the surface of earth.

Q.4. The distance of planet Jupiter from the sun 5.2 times that of Earth. Find the period of revolution of Jupiter around sun.

Q.5. Two satellites of a planet have periods 32 days and 256 days. If the radius of orbit of former is R, find the orbital radius of the latter.

Q.6. A sphere of mass 40kg is attracted by a second sphere of mass 15kg when their centres are 20 cm apart, with a force of 0.1 milligram weight. Calculate the value of gravitational constant.

Q.7. If the distance of Earth from the Sun were half the present value, how many days will make one year?

Q.8. A body of mass 1 kg is placed at a distance of 2m from another body of mass 10kg. At what distance from the body of 1 kg, another body of mass 5 kg be placed so that the net force of gravitation acting on the body of mass 1 kg is zero?

Q.9. The mass of Earth is 6 x 10²⁴ kg and that of moon is 7.4 x 10²² kg. If the distance between the Earth and the Moon is 3.84 x 10⁵ km, calculate the force exerted by Earth on the Moon. Given G = 6.7 x 10^–11 Nm²/kg².

Q.10. Two electrons each of mass 9.1 x 10^–31 kg are at a distance of 10 A⁰. Calculate the gravitational force of attraction between them. Given 1 A⁰=10^-10 m

Q.11. The gravitational force between force two objects is 100 N. How should the distance between these objects be changed so that force between them becomes 50 N?

Q.12. Two bodies A and B having masses 2kg and 4kg respectively are separated by 2m. Where should a body of mass 1kg be placed so that the gravitational force on this body due to bodies A and B is zero?

Q.13. Calculate the force of gravitation between two objects of masses 80kg and 1200 kg kept at a distance of 10 m from each other. Given G = 6.67 x 10^–11 Nm²/kg².

Q.14. Calculate the force of attraction between the Earth and the Sun, given that the mass of Earth is 6 x 10²⁴ kg and that of sun is 2 x 10³⁰ kg. The average distance between the two is 1.5 x 10¹¹ m.

Q.15. Calculate the gravitational force on a body of mass 1kg lying on the surface of earth. Given mass of earth is 6 x 10²⁴ kg and radius of earth is 6400km.

Q.16. A sphere of mass 25kg attracts another sphere of mass 24kg with a force of 0.1milligram weight. If distance between the centres of two spheres is 20cm, what is the value of G?

Q.17. If distance between two masses is quadrupled, what will be the new force of attraction between them? Given the initial gravitational pull is 9.8N.

Q.18. An electron of mass 9.1 x 10^–31kg is at a distance of 10^-10 m from a proton of mass 1.67 x 10^–27 kg. Calculate the gravitational force of attraction between them.

Q.19. The mass of Sun is 2 x 10³⁰ kg and mass of Earth is 6 x 10²⁴ kg. If the distance between the centres of Sun and Earth is 1.5 x 10⁸ km, calculate the force of gravitation between them.

Q.20. Two bodies A and B having masses 20kg and 40kg are separated by 10m. At what distance from body A should another body C of mass 15kg be placed so that net gravitational force on C is zero?

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