RAI SAHEB BHANWAR SINGH COLLEGE NASRULLAGANJ

1. RAI SAHEB BHANWAR SINGH
COLLEGE NASRULLAGANJ
SESSION – 2017-2018
CLASS – B.Sc. C.S. I YEAR
PRESENTATION ON
Gravitation self-energy of a uniform solid
sphere
SUBMITTED TO SUBMITTED BY
Mr. Gyanrao Dhote Pakshika Tanwar

2. Gravitation self-energy of a
uniform solid sphere
Let M be the mass and R be the radius of a solid sphere.
Since the entire mass of the sphere is uniformly
Distributed . Hence the density of material of sphere
Now let the central core of radius r of sphere be surrounded by a spherical
sell of thickness dr as shown in picture .
The mass of central core is m = 4/3 and mass spherical shell of
thickness dr is dm = 4 dr ƿ .

3. Clearly the work done in raising the spherical shell of thickness dr over the
sphere of radius r = gravitational potential energy of this system .
Now dW = -G . mass of the sphere . mass of the shell / r
or dW =
=
Hence work done in increasing the radius of sphere from r = 0 to r = R will
be the Self energy of sphere .

4. i.e.,
=
=
= =
since
This will be the gravitational self energy of uniform solid sphere of
mass M and radius R .