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Gravitation

Chapter 5 covers gravitation, including Kepler's Laws of planetary motion and the Universal Law of Gravitation. It defines key concepts such as escape velocity and gravitational potential, and includes derivations for variations in acceleration due to gravity with altitude and depth. The chapter also presents problems related to the gravitational effects on satellites and calculations involving the Earth's and Moon's gravity.

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ASHISH BEEDKAR
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4 views2 pages

Gravitation

Chapter 5 covers gravitation, including Kepler's Laws of planetary motion and the Universal Law of Gravitation. It defines key concepts such as escape velocity and gravitational potential, and includes derivations for variations in acceleration due to gravity with altitude and depth. The chapter also presents problems related to the gravitational effects on satellites and calculations involving the Earth's and Moon's gravity.

Uploaded by

ASHISH BEEDKAR
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Chapter 5: Gravitation

Q.1 State and Explain Kepler’s Laws of planetary motion.


Q.2 State and Explain Universal Law of Gravitation.

Q.3 Definitions:
1. Escape Velocity.
2. Critical/Orbital Velocity.
3. Binding energy of an orbiting satellite.
4. Time period of a Satellite.
5. Gravitational potential.
6. Gravitational potential energy.

Q.4 Derivations and Graph:


1. Derive the formula for Variation in acceleration due to gravity with Altitude (height h).
2. Derive the formula for Variation in acceleration due to gravity with Depth (depth d).
3. Draw the graph for Variation in g due to depth and altitude from the Earth’s surface.
4. Derive the formula for Escape velocity of object from earth.
5. Derive the formula for Critical Velocity of Satellite orbiting earth.

Q.5 Answer the following:


1. Explain the projection of satellite and discuss various cases.
2. Why do astronauts in an orbiting satellite have a feeling of weightlessness?
Q.6 Show that the critical velocity of a body revolving in a circular orbit very close to the surface of a
𝐺𝜋𝜌
planet of radius R and mean 𝜌 is 2𝑅 √ 3
.

Q.7 An artificial satellite revolves around a planet in circular orbit close to its surface. Obtain the
formula for period of the satellite in terms of density ρ and radius R of planet.
Q.8 Derive the expression for time period of satellite (take r = R + h).
Q.9 Problems:
1. What would be the average duration of year if the distance between the Sun and the Earth becomes
(A) thrice the present distance. (B) Twice the present distance.
2. Calculate mass of the Earth from given data, Acceleration due to gravity g = 9.81m/s2 Radius of the
Earth RE = 6.37×106 m G = 6.67×10-11 N m2/kg2.
3. Calculate the acceleration due to gravity on the surface of moon if mass of the moon is 1/80 times
that of the Earth and diameter of the moon is 1/4 times that of the Earth (g =9.8 m/s2).
4. At what distance above the surface of Earth the acceleration due to gravity decreases by 10% of its
value at the surface? (Radius of Earth = 6400 km). Assume the distance above the surface to be small
compared to the radius of the Earth.
5. Calculate the value of acceleration due to gravity on the surface of Mars if the radius of
Mars = 3.4×103 km and its mass is 6.4×1023 kg.
6. Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial
satellite of mass 2000 kg orbiting at a height of 3600 km above the surface of the Earth. Given:-
G = 6.67×10-11 Nm2/kg2 R = 6400 km M = 6×1024 kg.
7. Find the gravitational force between the Sun and the Earth. Given Mass of the Sun = 1.99×1030 kg
Mass of the Earth = 5.98×1024 kg, the average distance between the Earth and the Sun = 1.5×1011 m.
8. Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface. M E =
5.98×1024 kg, RE = 6.4×106 m.

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