Gravitational Self energy of a Uniform hollow and solid sphere – Definition and Derivation .

It is the energy possessed by a body due to the interaction forces inside the body . This can be defined as the work done by external agent in assembling all the particles of a body in a definite shape and size or it is the work done in creating a body.

– gravitational self energy of a hollow sphere of mass M and radius R is given as
Uself = – GM²/2R

– gravitational self energy of the solid sphere of mass M and radius R is given as
Uself = – 3GM²/5R

Torricelli’s theorem ( Velocity of efflux ) : Principle , Derivation and sloved examples

According to Torricelli’s theorem -The velocity of efflux of a liquid issuing out of an orifice is the same as it would attain if allowed to fall freely through the vertical height between the liquid surface and orifice .
velocity of efflux v = ( 2gh )1/2

Note – The velocity of efflux is the velocity of escaping liquid relative to the container (but not necessarily relative to ground when the container moves ) .

Newton’s law of Universal Gravitation | Definition , Equation , Facts and Solved Examples.

The magnitude of the gravitational force F that two particles of masses  m1 and m2 , separated by a distance r ,  there exists an attraction , which is proportional to the product of their masses and inversely proportional to the square of distance between the exert force on each other is given by
F = Gm1m2 / r²
Where G is a constant , Called the universal gravitation constant . It’s value in SI units is G = 6.674×10-11 N.m²/kg².