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Physics · Class 11 Science

Ch 5Gravitation — Class 11 Physics, concept-first.

All material objects show a natural tendency to move towards the Earth -- a coconut falling from a tree, raindrops falling from clouds, a dropped pencil -- and, remarkably, every falling body accelerates towards the Earth at the SAME constant rate, irrespective of its own mass.

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Key concepts

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Variation of g with Latitude and Earth's Rotation

Because the Earth rotates about its polar axis, every point on its surface except the two poles is carried along a circular path, requiring a centripetal force that is supplied by PART of the gravitational attraction --…

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Chapter contents

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5.1

Introduction

All material objects show a natural tendency to move towards the Earth -- a coconut falling from a tree, raindrops falling from clouds, a dropped pencil -- and, remarkably, every falling body accelera…

5.2

Kepler's Laws

Kepler's laws of planetary motion describe the actual orbits followed by the planets around the Sun. Kepler published the first two laws in 1609 and the third in 1619, all derived purely from painstak…

5.3

Universal Law of Gravitation

Galileo had already shown that all objects, heavy or light, fall towards the Earth with the same acceleration when released from the same height near the surface.

5.4

Measurement of the Gravitational Constant (G)

The value of the universal gravitational constant G is determined experimentally, not derived theoretically, by directly measuring the (extremely small) gravitational force of attraction between two k…

5.5

Acceleration due to Gravity

Section 5.3 gave the gravitational force between two point masses as . Since the Earth is, to a very good approximation, a uniform sphere, its entire mass M can (by the shell theorem of section 5.3) b…

5.6

Variation in the Acceleration due to Gravity with Altitude, Depth, Latitude and Shape

The value m/s² is often quoted as though it were a fixed universal constant, but it is really only the acceleration due to gravity AT THE EARTH'S SURFACE, at a particular latitude, under an idealised…

5.6.1

(A) Variation in g with Altitude

Consider a body of mass m at the Earth's surface, where the acceleration due to gravity is . When the same body is raised to height h above the surface (Fig.

5.6.2

(B) Variation in g with Depth

The Earth can be modelled as built up from many thin, uniform, concentric spherical shells, one inside another, with the total mass M being the sum of all their individual masses.

5.6.3

(C) Variation in g with Latitude and Rotation of the Earth

So far g has been treated as though the Earth were a perfect, non-rotating sphere. In reality the Earth rotates about its polar axis (west to east) with angular velocity , and every point on its surfa…

5.7

Gravitational Potential and Potential Energy

In earlier study, potential energy was introduced as the energy an object possesses because of its POSITION or CONFIGURATION within a system -- 'configuration' referring to how the various parts/parti…

5.7.1

Expression for Gravitational Potential Energy

To find an explicit formula for gravitational potential energy, consider the work done AGAINST the Earth's gravitational force while displacing an object through a small displacement ; this work appea…

5.7.2

Connection of the Potential Energy Formula with mgh

The formula derived in the previous section is the EXACT expression for gravitational potential energy at any distance r from the Earth's centre.

5.7.3

Concept of Potential

From the gravitational potential energy formula , the factor depends only on the source mass M (the Earth, in this case) and the location r -- it does NOT depend on the particular test mass m being co…

5.7.4

Escape Velocity

When an object is thrown vertically upward, it rises to some height and then falls back, pulled down by the Earth's continuous gravitational attraction.

5.8

Earth Satellites

Objects that revolve around the Earth are called Earth satellites. The Moon is the Earth's only NATURAL satellite, moving in an almost circular orbit with a period of about 27.3 days.

5.8.1

Projection of Satellite

Launching an artificial satellite into a stable orbit requires giving it a very specific COMBINATION of speed and direction -- something a single-stage rocket cannot achieve, which is why a minimum of…

5.8.2

Weightlessness in a Satellite

Newton's second law, , applies to any object with a net force F producing an acceleration a. Consider a passenger standing on a weighing machine inside a lift (an inertial-frame analysis): regardless…

5.8.3

Time Period of a Satellite

The time period of a satellite is the time it takes to complete exactly one full revolution around the Earth.

5.8.4

Binding Energy of an Orbiting Satellite

A satellite moving in a stable circular orbit possesses BOTH kinetic energy (from its orbital motion) and potential energy (from its position in the Earth's gravitational field), and the sum of the tw…

More questions

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+Show 4 questions4 questions
  1. Q1The value of acceleration due to gravity is maximum at (A) the equator of the Earth. (B) the centre of the Earth. (C) the pole of the Earth.…Free
  2. Q2The weight of a particle at the centre of the Earth is (A) infinite. (B) zero. (C) same as that at other places. (D) greater than at the pol…Free
  3. Q3The gravitational potential due to the Earth is minimum at (A) the centre of the Earth. (B) the surface of the Earth. (C) a point inside the…Preview
  4. Q4The binding energy of a satellite revolving around a planet in a circular orbit is $3\times10^9$ J. Its kinetic energy is (A) $6\times10^9$…Preview
+Show 15 questions15 questions
  1. Q5State Kepler's law of areas.Free
  2. Q6State Kepler's law of period.Free
  3. Q7What are the dimensions of the universal gravitational constant?Free
  4. Q8Define binding energy of a satellite.Preview
  5. Q9What do you mean by a geostationary satellite?Preview
  6. Q10State Newton's law of gravitation.Preview
  7. Q11Define escape velocity of a satellite.Preview
  8. Q12What is the variation in acceleration due to gravity with altitude?Preview
  9. Q13On which factors does the escape speed of a body from the surface of the Earth depend?Preview
  10. Q14As we go from one planet to another planet, how will the mass and weight of a body change?Preview
  11. Q15What is the periodic time of a geostationary satellite?Preview
  12. Q16State Newton's law of gravitation and express it in vector form.Preview
  13. Q17What do you mean by gravitational constant? State its SI units.Preview
  14. Q18Why is a minimum two stage rocket necessary for launching of a satellite?Preview
  15. Q19State the conditions for various possible orbits of a satellite depending upon the tangential speed of projection.Preview
+Show 16 questions16 questions
  1. Q20Derive an expression for critical velocity of a satellite.Free
  2. Q21State any four applications of a communication satellite.Free
  3. Q22Show that acceleration due to gravity at height h above the Earth's surface is $g_h=\dfrac{gR^2}{(R+h)^2}$.Free
  4. Q23Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.Preview
  5. Q24Derive an expression for binding energy of a body at rest on the Earth's surface.Preview
  6. Q25Why do astronauts in an orbiting satellite have a feeling of weightlessness?Preview
  7. Q26Draw a graph showing the variation of gravitational acceleration due to the depth and altitude from the Earth's surface.Preview
  8. Q27At which place on the Earth's surface is the gravitational acceleration maximum? Why?Preview
  9. Q28At which place on the Earth's surface is the gravitational acceleration minimum? Why?Preview
  10. Q29Define the binding energy of a satellite. Obtain an expression for binding energy of a satellite revolving around the Earth at a certain alt…Preview
  11. Q30Obtain the formula for acceleration due to gravity at the depth 'd' below the Earth's surface.Preview
  12. Q31State Kepler's three laws of planetary motion.Preview
  13. Q32State the formula for acceleration due to gravity at depth 'd' and at altitude 'h'. Hence show that their ratio is equal to $\dfrac{g_d}{g_h…Preview
  14. Q33What is critical velocity? Obtain an expression for critical velocity of an orbiting satellite. On what factors does it depend?Preview
  15. Q34Define escape speed. Derive an expression for the escape speed of an object from the surface of the Earth.Preview
  16. Q35Describe how an artificial satellite using a two stage rocket is launched in an orbit around the Earth.Preview
+Show 12 questions12 questions
  1. Q36At what distance below the surface of the Earth does the acceleration due to gravity decrease by 10% of its value at the surface, given radi…Free
  2. Q37If the Earth were made of wood, the mass of the wooden Earth would have been 10% as much as it is now (without change in its diameter). Calc…Free
  3. Q38Calculate the kinetic energy, potential energy, total energy and binding energy of an artificial satellite of mass 2000 kg orbiting at a hei…Free
  4. Q39Two satellites A and B are revolving around a planet. Their periods of revolution are 1 hour and 8 hours respectively. The radius of orbit o…Preview
  5. Q40Find the gravitational force between the Sun and the Earth. Given Mass of the Sun = $1.99\times10^{30}$ kg, Mass of the Earth = $5.98\times1…Preview
  6. Q41Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = $5.98\times10^{24}$ kg, R = 6400 km).Preview
  7. Q42Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth's surface. $M_E=5.98\times10^{24}$ kg, R = $6.4\times10…Preview
  8. Q43Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = $3.4\times10^3$ km and its mass is $6.4\ti…Preview
  9. Q44A planet has mass $6.4\times10^{24}$ kg and radius $3.4\times10^6$ m. Calculate the energy required to remove an object of mass 800 kg from…Preview
  10. Q45Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = $6\times10^{24}$ kg, Radius of the Eart…Preview
  11. Q46A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and…Preview
  12. Q47What is the gravitational potential due to the Earth at a point which is at a height of $2R_E$ above the surface of the Earth? Mass of the E…Preview