Gravitation

Question 1

Gravitation

Answer 1

Force of attraction between any two bodies in the universe

Question 2

Gravity

Answer 2

Force of attraction between the earth and any object lying on or near its surface

Question 3

Newton’s law of gravitation

Answer 3

Every partice in the universe attracts every other particle with a force which is directly proportional to the produce of their masses and inversely proportional to the square of the distances between them
F = Gm1 m2 / r^2

Question 4

G value

Answer 4

6.67 * 10 ^ -11 Nm^2 / kg^2

Question 5

Gravitation in vector format

Answer 5

F = -G m1 m2 * (r cap) / r^2

Question 6

Principle of Superposition of gravitational forces

Answer 6

Gravitational force between two masses acts independently and uninfluenced by the presence of other bodies. Hence, the resultant gravitational force acting on a particle due to a number of masses is the vector sum of the gravitational forces exerted by the individual masses on the given particle

Question 7

Shell Theorem

Answer 7

• If a point mass lies outside a uniform spherical shell with a spherically symmetric internal mass distribution, the shell attracts the point mass as if the entire mass of the shell were concentrated at its centre
• If a point mass lies inside a uniform spherical shell, the gravitational force on the point mass is zero. But if a point mass lies inside a homogeneous solid sphere, the force on the point mass acts towards the centre of the sphere.

Question 8

Mass of earth in terms of density

Answer 8

M = ro * V = ro * 4/3 pi * r^3

Question 9

Acceleration due to g on different points on earth

Answer 9

1. Above earth: F = GMm / r^2
2. Below earth’s surface: F = GMm / R^3 * r
3. At points on earth’s surface: F = GMm / R^2

Question 10

Relation between g and G

Answer 10

g = GMm / R^2

Question 11

Variation of g with altitude derivation

Answer 11

gh = g (1 - 2h / R)

Question 12

Variation of g with depth

Answer 12

g = g(1 - d / R)

Question 13

Formulas of g variation

Answer 13

With altitude:
1. g = g * R^2 / (R + h)^2
2. g = g (1 - 2h / R)
With depth:
1. g = g (1 - d / R)
With radius
1. Inversely proportional

Question 14

Variation of g with shape of Earth

Answer 14

• Flat at poles and bulges at equatior
• Since g is inversely proportional to R^2
• Re > Rp or ge < gp

Question 15

Gravitational Field

Answer 15

Space surrounding a material body within its gravitational force of attraction can be experienced

Question 16

Gravitational Field intensity

Answer 16

At any point in the gravitational field due to a given mass is defined as the force experienced by a unit mass placed at that point providede the presence of unit mass does not disturb the original gravitational field

Question 17

gravitational field intensity formula

Answer 17

E = F / m = GM / r^2 = g

Question 18

Gravitational Potential Energy

Answer 18

Energy associated with it due to its position in the gravitational field of another body and is measured by the amount of work done in bringing a body from infinity to a given point in the gravitational field of the other

Question 19

Gravitational potential energy derivation

Answer 19

U = -GMm / r

Question 20

Gravitational Potential

Answer 20

Potential energy associated with a unit mass due to its position in the gravitational field of another body
V = -GM / r

Question 21

Total energy of a body in a gravitational field

Answer 21

E = KE + PE = 1/2 mv^2 + (-GMm / R)

Question 22

Escape Velocity

Answer 22

Minimum velocity with which a body must be projected vertically upwards in order that it may just escape the gravitational field of the earth

Question 22

Escape velocity formulas and derivations

Answer 22

v = root (2 GM / R) = root (2gR) = root (8pi ro G R^2 / 3)

Question 23

Escape velocity at a height h

Answer 23

ve = root (2g (re)^2 / (re + h))
re = rad. of earth

Question 24

Orbital Velocity

Answer 24

Velocity required to put the satelleite into its orbit around the earth

Question 26

Derivation of orbital velocity and formulas

Answer 26

v = root (GM / R + h) = root (gR^2 / R + h) = R root (g / R + h)

Question 27

Relation between orbital and escape velocity

Answer 27

ve = (root 2) (vo)

Question 28

Derive time period and all for satellite

Answer 28

T = 2pi [Root (R + h)^3 / gR^2]

Question 29

Total energy of satellite

Answer 29

E = GMm / 2r {-Gmm / r + 1/2 Gmm / r}

Question 30

Binding energy of a satellite

Answer 30

Gmm / 2r {energy required by a satellite to leave its orbit around the earth and escape to infinity}

Question 31

Kepler's Laws of Motion

Answer 31

1. dL / dt = 0 (L is constant) 2. Delta A / Delta T = constant 3. T1^2 / T2^2 = R1^3 / R2^3