Two particle of masses `m` and `2m` are at a distance `3r` apart at the ends of a straight line `AB`. `C` is the centre of mass of the system. The magnitude of the gravitational force on a unit mass placed at `C` due to the masses is

a solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m is placed on the line joining the two centers as a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if a). rltxlt2r, b). 2rltxlt2R and c). xgt2R .

a solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m is placed on the line joining the two centers as a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if a). rltxlt2r , b). 2rltxlt2R and c). xgt2R .

Two particles of masses 2 m and 3 m are at a distance .d. apart. Under their mutual gravitational force, they start moving towards each other. The accelaration of their centre of mass when they are d/2 apart is

Two bodies of masses M_(1) and M_(2) , are placed at a distance R apart. Then at the position where the gravitational field due to them is zero, the gravitational potential is