1. Show that the principle of conservation of angular momentum applied to planetary motion leads to the law of constant areal velocity.

2. What are the values of potential energy of a body taking reference level at (i) the earth's surface and (ii) infinity?

3. Define escape velocity and geosynchronous orbit.

4. Show that for an external point a spherical shell behaves as if whole mass is concentrated at the centre deriving the expression for gravitational potential due to a spherical shell outside the shell.

5. The mass of the moon is about 0-013 ne times the mass of the earth and the distance of centre of the moon from centre of the earth is about 60 times of radius of the earth. Find the distance of centre of mass of earth-moon system from the centre of the earth. Take radius of the earth is 6400 km.

6. Show that the gravitational potential due to a solid sphere, inside the sphere is 3/2 times that on the surface of the sphere.

7. Two bodies of masses m₁ and m2 are interacting through a central force. Show that their equation of motion can always be reduced to single body equation.

8. Find the intensity of gravitational field due to a thin spherical shell at a point outside the shell.

9. What is the difference between inertial and gravitational mass?

10. Find the gravitational potential on the surface of a spherical cell.

11. The earth mass is 80 times that of the vaw moon and their diameters are 12800 km and 3200 km respectively. What is the value of g on the moon, if g on the earth is 9.8 m/s²?

12. Describe briefly about gravitational potential. Show that gravitational potential at the centre of a solid sphere is times that on the surface.

13. State Kepler's three laws of planetary motion.

14. What is geosynchronous orbit and global positioning system?

15. Differentiate between inertial mass and gravitational mass.

16. Calculate gravitational potential on the surface of a spherical shell.

17. Assuming the earth to be a sphere of radius R, show that gravitational field intensity and potential at any point on the earth's surface can be expressed as g and gR respectively, where g is the acceleration due to gravity.

18. Define gravitational potential. Show that the gravitational at the centre of a solid sphere is 3/2 times that on the surface.

19. Give a brief description of GPS.

20. Obtain Kepler's 3rd law from Newton's law of gravitation.

21. Define gravitational potential and gravitational potential energy.

22. What is the difference between inertial mass and gravitational mass?

23. Describe in brief global positioning system (GPS).

24. Obtain an expression for gravitational potential due to a solid sphere at a point outside the sphere. What will be the potential when the point lies on the surface of the sphere?

25. Write the characteristic of the motion of a particle in a central force field. State Kepler's laws of planetary motion.

26. Explain in brief how a satellite may be placed in its orbit round the earth, and find an expression for its orbital velocity and time period.

28. Given,
radius of the earth is R=6·37×108 cm
mean density of the earth = 5·53 g/cm³
gravitational constant = 6.66×10⁻⁸ CGS units
Using the above data, calculate the gravitational potential on the surface of the earth. Explain geosynchronous orbit and weightlessness

29. Define central force. Give one example.

30. State Kepler’s laws of planetary motion.

31. Explain weightlessness.

32. State Newton’s law of gravitation. Find the gravitational potential inside and outside of a spherical shell.

33. The potentials within two homogeneous shells of same surface density are in the ratio 1 : 2
Calculate the ratio of their radii.

34 Define angular momentum of a particle. Show that when a particle moves under central force, angular momentum is a constant of motion.

35. Write short notes on the following :
(i) Escape velocity
(ii) Global Positioning System (GPS)