Gravitation Flashcards
Gravitational Force
Gm1m2/r2
Gravitational force is medium independent
As well as conservative
True or false
Sphere can be considered a point mass
True. But rods cannot be considered so
Gravitational net force can be calculated by
1}Simple addition
2}Vector addition
Vector addition
for rods we need to use
Integration
Acceleration due to gravity
GM/R2
As we go above the surface it becomes
g upon square of 1 plus h by r
As we go below the surface it becomes
g times 1 minus d by r
Axial rotation affects in the pattern
g minus r(omega)^2cos sq phi
at equator phi = 0
hence g= g minus r omega sq i.e. min
at poles phi = 90
hence g= g i.e. max
Gravitational field is defined as
the space around a mass or system in which any other test mass experiences a grav. force
Gravitational field strength is defined as
Force experienced by a unit test mass placed at a point in a grav. field
Field due to point mass
GM by r sq
Field due to uniform solid sphere
At external
GM by r sq
Field due to uniform solid sphere
At internal point
GM r by R cube
Field due to uniform spherical shell
at external
GM by r sq
Field due to uniform spherical shell
at internal
zero
Field due to uniform circular ring at a point on its axis
GMr by (R sq + r sq )^(3/2)
Gravitational Potential
Work done by gravitational force in moving a test mass from one point to another point.
Potential due to point mass
minus GM by r
Potential due to solid sphere uniform
At external
minus GM by r
Potential due to solid sphere uniform
at surface
Minus GM by R
Potential due to solid sphere uniform
at internal
minus GM by R cube into(1.5 R sq - 0.5 r sq)
Potential due to uniform thin spherical shell
at external
minus GM by r
Potential due to uniform thin spherical shell
at internal
minus GM by R
potential due to uniform ring at some point on its axis
minus GM upon underroot of R sq + r sq
potential can be added
Directly (Simple addition)
Field strength can be added
BY vector addition
V equals to
minus integration of Edx
E equals to
minus dV by dR
Gravitational potential energy
minus of work done by gravitational forces in bringing a body from infinity to present position.
Formula for gravitational potential
minus of integration of F.dr {Limits: infinity to r}
Gravitational potential energy of a two particle system
minus Gm1m2 by r
For n particle system
Just add up all possible two member pairs
P.S. there will be { n into n-1 by 2 } no of pairs
Gravitational potential energy of a particle on earth’s surface
minus of GMm by r
Difference in potential energy
mgh by (1 plus h by R)
Binding Energy
|Total energy|
Escape velocity
underroot of (2gR)
