#### IIT (NTSE/Olympiad)

# Gravitation

__Gravitational Potential Energy__

__Gravitational Potential Energy__

a) It is defined as the space around the attracting body, in which its attraction (gravitational) can be experienced.

b)

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/sec

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

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 [M

e) Gravitational potential is a scalar quantity.

f) At r = ∞, V = 0.

(1) E

(2) V

(i) If point P is situated outside the sphere, then OP = r > R

(1) E

(2) V

(ii) If point P is situated on the surface of sphere, then OP = r = R

(1) E

(iii) If point P is situated inside the sphere, then OP = r < R

(1) E

(2) V

b)

**- it is defined as the force experienced by unit mass place at any point in the gravitational field.***Intensity of gravitational field or gravitational field strength*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/sec

^{2}. Dimension formula is [M^{0}L^{1}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 expressionE = = 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 [M

^{0}L^{2}T^{-2}].e) Gravitational potential is a scalar quantity.

f) At r = ∞, V = 0.

(1) E

_{in}= 0(2) V

_{in}= -**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) E

_{out}= -(2) V

_{out}= -(ii) If point P is situated on the surface of sphere, then OP = r = R

(1) E

_{surface}= -(2) V_{surface}= -(iii) If point P is situated inside the sphere, then OP = r < R

_{e}(1) E

_{in }= -(2) V

_{in}= -**Note :**V_{centre}= 1.5 V_{surface}**Graphical Representation of Gravitational Field Intensity For Hollow Sphere****Graphical Representation of Gravitational potential For HollowSphere****For Solid Sphere****For Solid Sphere**#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION