1. Let us consider the case when the point mass A, is at the centre of the hollow thin shell.
2. In this case as every point on the shell is equidistant from A, all points exert force of equal magnitude on A but the directions of these forces are different.
3. Consider the forces on A due to two diametrically opposite points on the shell.
4. The forces on A due to them will be of equal magnitude but will be in opposite directions and will cancel each other.
5. Thus, forces due to all pairs of points diametrically opposite to each other will cancel and there will be no net force on A due to the shell.
6. When the point object is situated elsewhere inside the shell, the situation is not symmetric. However, gravitational force varies directly with mass and inversely with square of the distance.
7. When the point object is situated elsewhere inside the shell, the situation is not symmetric. However, gravitational force varies directly with mass and inversely with square of the distance.
8. Thus, some part of the shell may be closer to point A, but its mass is less. Remaining part will then have larger mass but its centre of mass is away from A.
9. In this way, mathematically it can be shown that the net gravitational force on A is still zero, so long as it is inside the shell.
10. Hence, the gravitational force at any point inside any hollow closed object of any shape is zero.
