## Unit – I B |

## Newton’s Law of Gravitation Problems:

### Formulae

- Calculate the force of attraction between two metal spheres each of mass 90 kg, if the distance between their centres is 40 cm. Given G = 6.67 x 10
^{-11}N m^{2}/kg^{2}. - Find the gravitational force of attraction between the moon and the earth if the mass of the moon is 1/81 times the mass of earth. G = 6.67 x 10
^{-11}N m^{2}/kg^{2}, radius of moon’s orbit is 3.58 x 10^{5}km. Mass of the earth = 6 x 10^{24}Kg. - Two bodies of masses 5 kg and 6 x 10
^{24}kg are placed with their centres 6.4 10^{6}m apart. Calculate the force of attraction between the two masses. Also find the initial acceleration of two masses assuming no other forces act on them. - A sphere of mass 40 kg is attracted by another spherical mass of 15 kg by a force of 9.8 x 10
^{-7}N when the distance between their centres is 0.2 m. Find G. - A sphere of mass 100 kg is attracted by another spherical mass of 11.75 kg by a force of 19.6 x 10
^{-7}N when the distance between their centres is 0.2 m. Find G. - Distance of a planet from the earth is 2.5 x 10
^{7}km and the gravitational force between them is 3.82 x 10^{18}N. Mass of the planet and earth are equal, each being 5.98 x 10^{24}kg. Calculate the universal gravitation constant. - Three 5 kg masses are kept at the vertices of an equilateral triangle each of side of 0.25 m. Find the resultant gravitational force on any one mass. G=6.67 x 10
^{-11}S.I. units.

### Answers:

- 3.377 x 10-6 N
- 2.213 x 1020 N
- 48.85 N, 9.77 m/s2, 8.142 x 10-24 m/s2
- 6.533 x 10
^{-11}Nm^{2}/kg^{2} - 6.672 x 10
^{-11}Nm^{2}/kg^{2} - 6.676 x 10
^{-11}Nm^{2}/kg^{2} - 4.621 x 10-8 N towards the centroid