The gravitational field due to an uniform solid sphere of mass M and radius a at the centre of the sphere is

Gravitational field due to a solid sphere

Gravitational field due to a solid sphere

A uniform solid of valume mass density rho and radius R is shown in figure. (a) Find the gravitational field at a point P inside the sphere at a distance r from the centre of the sphere. Represent the gravitational field vector vec(l) in terms of radius vector vec(r ) of point P. (b) Now a spherical cavity is made inside the solid sphere in such a way that the point P comes inside the cavity. The centre is at a distance a from the centre of solid sphere and point P is a distance of b from the centre of the cavity. Find the gravitational field vec(E ) at point P in vector formulationand interpret the result.

A uniform solid of valume mass density rho and radius R is shown in figure. (a) Find the gravitational field at a point P inside the sphere at a distance r from the centre of the sphere. Represent the gravitational field vector vec(l) in terms of radius vector vec(r ) of point P. (b) Now a spherical cavity is made inside the solid sphere in such a way that the point P comes inside the cavity. The centre is at a distance a from the centre of solid sphere and point P is a distance of b from the centre of the cavity. Find the gravitational field vec(E ) at point P in vector formulationand interpret the result.

Gravitational Field Due To Spheres

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mass M and radius R is placed directly above a uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of d = sqrt(3)R from the centre of the sphere. The gravitational attraction between the sphere and the ring is

Find the moment of inertia of a uniform sphere of mass m and radius R about a tangent if the spheres (1) solid (ii) hollow?