IIT (NTSE/Olympiad)  

Gravitation

Gravitational Potential Energy

a) It is defined as the space around the attracting body, in which its attraction (gravitational) can be experienced.
b) Intensity of gravitational field or gravitational field strength - it is defined as the force experienced by unit mass place at any point in the gravitational field.
c) Gravitational field is a vector quantity.
d) Suppose a body of mass M is placed at a distance r, then intensity of gravitational field

at point P will be
e) Unit of gravitational field strength is Newton/kg or m/sec2. Dimension formula is [M0 L1 T-2].
f) As the distance (r) increases, gravitational field strength decreases. At r = ∞, value of intensity of gravitational field becomes zero.
g) Intensity of gravitational field at a distance r form the centre of earth is E = = g . I
NOTE : From this expression

E = = g, it is clear that the intensity of gravitational field at any place is equal to acceleration due to gravity.
h) Change of intensity of gravitational field due to a point mass with respect to distance -
E =
i) Relation between gravitational field and gravitational potential -
E = - ΔV ⇒ E = -

a) The work done in bringing a unit mass form infinity to a point in the gravitational field is called the 'gravitational potential' at that point.
b) Gravitational potential at a point P distance r form a point mass 'M' will beV = -

c) Unit of Gravitational potential is Joule/kg
d)Dimensional formula of Gravitational potential is [M0 L2 T-2].
e) Gravitational potential is a scalar quantity.
f) At r = ∞, V = 0.
(1) Ein = 0
(2) Vin = -
Note : Gravitational field intensity inside a hollow sphere is zero but gravitational potential is constant and is equal to the potential at the surface.
b) Solid Sphere : Let OP = r
(i) If point P is situated outside the sphere, then OP = r > R
(1) Eout = -
(2) Vout = -
(ii) If point P is situated on the surface of sphere, then OP = r = R
(1) Esurface = -(2) Vsurface = -
(iii) If point P is situated inside the sphere, then OP = r < Re
(1) Ein = -
(2) Vin = -
Note : Vcentre = 1.5 Vsurface
Graphical Representation of Gravitational Field Intensity For Hollow Sphere

Graphical Representation of Gravitational potential For HollowSphere

For Solid Sphere

For Solid Sphere


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