Gravitation

Question 1

Acceleration due to gravity

Answer 1

g= (GM)/R^2

R-radius of Earth
M-mass of Earth

Question 2

Variation of ‘g’ with height

Answer 2

g’ = g/[(1+h/R)^2]

h

Question 3

Variation of ‘g’ with depth

Answer 3

g’ = g*(1-h/R)

Question 4

Variation of ‘g’ due to rotation of Earth

Answer 4

g’ = g - R(wcos@)^2

@-latitude

Question 5

g at poles

Answer 5

g

Question 6

g at equator

Answer 6

g - R*w^2

Question 7

Orbital Speed

Answer 7

vo = (GM/a) ^0.5

a= R+h

Question 8

Time period of satellite

Answer 8

T= [(4||^2a^3)/GM]^0.5

Question 9

Angular momentum of satellite

Answer 9

(m^2GM*a)^0.5

Question 10

Total energy of satellite

Answer 10

TE= -GMm/2a

Question 11

Binding Energy

Answer 11

BE = GMm/2a = -TE

Question 12

Escape velocity

Answer 12

ve >= (2gR)^ 0.5

ve >= (2GM/R) ^0.5

Question 13

Relationship between escape velocity and orbital speed

Answer 13

ve >= (2^0.5) * vo

Question 14

Escape velocity at earths surface

Answer 14

11.6 km/s

Question 15

Gravitational field due to point mass

Answer 15

Eg = -GM/r^2 *er

Question 16

Gravitational field at axial point of circular ring

Answer 16

Eg = GMx/[(a^2+x^2)^3/2]

Question 17

Gravitational field at an axial point of circular disc

Answer 17

[2GM*(1-cos@)]/a^2

Question 18

Gravitational field inside a uniform spherical shell

Answer 18

0

Question 19

Gravitational field at a distance ‘r’ from a uniform spherical shell

Answer 19

GM/r^2

Question 20

Gravitational field inside a uniform spherical sphere

Answer 20

GMx/r^3

Question 21

Gravitational field at a distance ‘x’ from a uniform spherical sphere

Answer 21

GM/x^2

Question 22

Graph for gravitational field of uniform solid sphere

Answer 22

/|(
/ | (
/ | (

X axis- distance r
Y axis- gravitational field

Question 23

Gravitational potential of point mass

Answer 23

-GM/r

Question 24

Gravitational potential at axial point of uniform ring

Answer 24

-GM/(r^2+x^2)^0.5

Question 25

Gravitational potential Inside a uniform shell

Answer 25

-GM/r

Equipotential surface

Question 26

Gravitational potential outside uniform shell at a distance R

Answer 26

-GM/R

Question 27

Gravitational potential inside uniform solid sphere

Answer 27

-[GM(3r^2 - x^2)]/(2r^3)

Question 28

Gravitational potential outside uniform solid sphere

Answer 28

-GM/r