Gravitation Flashcards
Who recognised the fact that all bodies irrespective of their masses are accelerated towards the earth with a constant acceleration?
Galileo
Who gave the geocentric model?
Ptolemy gave the geocentric model in which all celestial bodies revolved around the Earth.
Who gave the heliocentric model?
Originally Aryabhatta mentioned its. A thousend years later a monk named Nicolas Copernicus stated it as: A model in which planets moved in circles around a fixed central sun.
Mention the Kepler’s Laws.
1.Law of Orbits: all planets move in elliptical orbits with the sun situated at one of the foci of the ellipse. This law was the deviation from the copernicus model which allowed only circular orbits.
2.Law of Areas: the line that joints any planet to the sun areas in equal intervals of time.
∆A/∆T.
3.Law of Periods: the square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.
T² ∝ a³
State the Universal Law of Gravitation.
It states that every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F = G(mM)/r²
Where, G is universe gravitational constant: 6.67 × 10-¹¹
We have to be careful since the law refers to point masses whereas we deal with extended objects which have finite size. If we have a collection of point masses the force on any one of them is the vector sum of the gravitational force exerted by the other point masses.
Show how Newton arrived at expression for Universal Law of Gravitation.
.
Show how Kepler arrived at the expression for his Law of Areas/ how Area sweeped by time period is constant according to Kepler’s Law of Areas.
.
Explain the special cases for gravitational force between extended objects and point size objects.
- The force of attraction between a hollow spherical shell of uniform density and point mass situated outside is just as ig the entire mass of the shell is concentrated at the centre of the shell.
- The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is zero. This is because the forces inside the shell from different points attracting the mass cancel each other out completely.
What is the value of G?
6.67 × 10¹¹ Nm²/kg²
Explain acceleration due to gravity.
When an object falls freely towards the surface of earth from a certain height, then its velocity changes and this change in velocity produces acceleration in the object which is known as acceleration due to gravity denoted by g. The value of acceleration due to gravity on Earth is 9.8m/s²
Explain The Cavendish Experiment.
The Cavendish Experiment (1797–1798) was conducted by Henry Cavendish to measure the gravitational attraction between masses and determine the density of the Earth. He used a torsion balance, consisting of a suspended wooden rod with two small lead spheres at its ends and two large lead spheres nearby. The gravitational force between the spheres caused the rod to twist, and by measuring this movement, Cavendish calculated the force of gravity and the Earth’s mass. His experiment indirectly led to the first accurate estimate of the gravitational constant (G) and helped establish the value of Earth’s density, making it a crucial milestone in physics.
Give expression for Acceleration due to gravity above the surface of Earth.
g(h) =≈ g[1-((2h)/R)]
Derive expression for Acceleration due to gravity above the surface of Earth.
.
Give the expression for Acceleration due to gravity below the surface of Earth.
g(d) =≈ g[1-(d/R)]
Derive the expression for Acceleration due to gravity above the surface of Earth
.
Gravitational Potential Energy.
Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field.
W = -GmM[(1/r)-(1/R)]
W(r) = -GmM/r + Vo
Where, Vo = Vnot = PE at ∞ = constant = 0 generally
Derive expression for Gravitational Potential Energy.
.
Define Gravitational Potential.
The gravitational potential due to the gravitational force of the Earth is defined as the potential energy of a particle at that point.
V = -Gm/r
Define Escape Speed/Velocity.
Minimum velocity a body must acquire to escape gravitational field.
v(min) = √2gR = √2GM/R
Derive expression for Escape Velocity.
.
Escape velocity of moon is _________________ than Earth.
5 times smaller.
Define Earth Satellites. Give expressions for their Time Period and Energy.
Earth Satellites are objects which revolve around the Earth.
T = [2π(R+h)³/²]/√GM
Special Case: (When satellite is very close (R + h) ≈ R)
T = 2π√R/g
KE = [m(GM)/(R+h)]/2
PE = (-GmM)/(R+h)
TE = KE + PE = [-GMm]/[2(R+h)]
Also, PE = 2KE
