# Balbharati solutions for Physics 11th Standard Maharashtra State Board chapter 5 - Gravitation [Latest edition]

## Chapter 5: Gravitation

Exercises
Exercises [Pages 97 - 99]

### Balbharati solutions for Physics 11th Standard Maharashtra State Board Chapter 5 Gravitation Exercises [Pages 97 - 99]

Exercises | Q 1. (i) | Page 97

Choose the correct option.

The value of acceleration due to gravity is maximum at ________.

• the equator of the Earth

• the center of the Earth

• the pole of the Earth

• slightly above the surface of the Earth

Exercises | Q 1. (ii) | Page 97

Choose the correct option.

The weight of a particle at the center of the Earth is _______.

• infinite

• zero

• same as that at other places

• greater than at the poles

Exercises | Q 1. (iii) | Page 97

Choose the correct option.

The gravitational potential due to the Earth is minimum at _______.

• the center of the Earth

• the surface of the Earth

• points inside the Earth but not at its center.

• infinite distance

Exercises | Q 1. (iv) | Page 97

Choose the correct option.

The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 109 J. It's kinetic energy is ______.

• 6 × 109 J

• –3 × 109 J

• –6 × 10+9 J

• 3 × 10+9 J

Exercises | Q 2. (i) | Page 97

State Kepler’s law of equal areas.

Exercises | Q 2. (ii) | Page 97

State Kepler’s law of the period.

Exercises | Q 2. (iii) | Page 97

What are the dimensions of the universal gravitational constant?

Exercises | Q 2. (iv) | Page 97

Define the binding energy of a satellite.

Exercises | Q 2. (v) | Page 97

What do you mean by geostationary satellite?

Exercises | Q 2. (vi) | Page 97

State Newton’s law of gravitation.

Exercises | Q 2. (vii) | Page 97

Define the escape velocity of a satellite.

Exercises | Q 2. (viii) | Page 97

What is the variation in acceleration due to gravity with altitude?

Exercises | Q 2. (ix) | Page 97

On which factors does the escape speed of a body from the surface of Earth depend?

Exercises | Q 2. (x) | Page 97

As we go from one planet to another planet, how will the mass and weight of a body change?

Exercises | Q 2. (xi) | Page 97

What is periodic time of a geostationary satellite?

Exercises | Q 2. (xii) | Page 97

State Newton’s law of gravitation and express it in vector form.

Exercises | Q 2. (xiii) | Page 97

What do you mean by a gravitational constant? State its SI units.

Exercises | Q 2. (xiv) | Page 97

Why is a minimum two-stage rocket necessary for launching of a satellite?

Exercises | Q 2. (xv) | Page 97

State the conditions for various possible orbits of satellite depending upon the horizontal speed of projection.

Exercises | Q 3. (i) | Page 98

Answer the following question in detail.

Derive an expression for the critical velocity of a satellite.

Exercises | Q 3. (ii) | Page 98

Answer the following question in detail.

State any four applications of a communication satellite.

Exercises | Q 3. (iii) | Page 98

Answer the following question in detail.

Show that acceleration due to gravity at height h above the Earth’s surface is "g"_"h" = "g"("R"/"R + h")^2

Exercises | Q 3. (iv) | Page 98

Answer the following question in detail.

Draw a well labelled diagram to show different trajectories depending upon the tangential projection speed.

Exercises | Q 3. (v) | Page 98

Answer the following question in detail.

Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.

Exercises | Q 3. (vi) | Page 98

Answer the following question in detail.

Why an astronaut in an orbiting satellite has a feeling of weightlessness?

Exercises | Q 3. (vii) | Page 98

Answer the following question in detail.

Draw a graph showing the variation of gravitational acceleration due to the depth and altitude from the Earth’s surface.

Exercises | Q 3. (viii) | Page 98

Answer the following question in detail.

At which place on the Earth’s surface is the gravitational acceleration maximum? Why?

Exercises | Q 3. (viii) | Page 98

Answer the following question in detail.

At which place on the Earth’s surface is the gravitational acceleration minimum? Why?

Exercises | Q 3. (x) | Page 98

Answer the following question in detail.

Derive an expression for variation in gravitational acceleration of the Earth at with latitude.

Exercises | Q 3. (xi) | Page 98

Define the binding energy of a satellite.

Exercises | Q 3. (xi) | Page 98

Answer the following question in detail.

Obtain an expression for the binding energy of a satellite revolving around the Earth at a certain altitude.

Exercises | Q 3. (xii) | Page 98

Answer the following question in detail.

Obtain the formula for the acceleration due to gravity at the depth ‘d’ below the Earth’s surface.

Exercises | Q 3. (xiii) | Page 98

Answer the following question in detail.

State Kepler’s three laws of planetary motion.

Exercises | Q 3. (xiv) | Page 98

Answer the following question in detail.

State the formula for the acceleration due to gravity at depth ‘d’ and altitude ‘h’. Hence show that their ratio is equal to (("R - d")/("R - 2h")) by assuming that the altitude is very small as compared to the radius of the Earth.

Exercises | Q 3. (xv) | Page 98

Answer the following question in detail.

What is a critical velocity?

Exercises | Q 3. (xv) | Page 98

Answer the following question in detail.

Obtain an expression for the critical velocity of an orbiting satellite. On what factors does it depend?

Exercises | Q 3. (xvi) | Page 98

Answer the following question in detail.

Show that acceleration due to gravity at height h above the Earth’s surface is "g"_"h" = "g"("R"/"R + h")^2

Exercises | Q 3. (xvii) | Page 98

Answer the following question in detail.

Define escape speed.

Exercises | Q 3. (xvii) | Page 98

Answer the following question in detail.

Derive an expression for the escape speed of an object from the surface of each.

Exercises | Q 3. (xviii) | Page 98

Answer the following question in detail.

Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.

Exercises | Q 4. (i) | Page 98

Answer the following question in detail.

At what distance below the surface of the Earth, the acceleration due to gravity decreases by 10% of its value at the surface, given the radius of Earth is 6400 km.

Exercises | Q 4. (ii) | Page 98

Answer the following question in detail.

If the Earth were made of wood, the mass of wooden Earth would have been 10% as much as it is now (without change in its diameter). Calculate escape speed from the surface of this Earth.

Exercises | Q 4. (iii) | Page 98

Answer the following question in detail.

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

Exercises | Q 4. (iv) | Page 98

Answer the following question in detail.

Two satellites A and B are revolving round a planet. Their periods of revolution are 1 hour and 8 hour respectively. The radius of orbit of satellite B is 4 × 104 km. Find radius of orbit of satellite A.

Exercises | Q 4. (v) | Page 99

Solve the following problem.

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.

Exercises | Q 4. (vi) | Page 99

Solve the following problem.

Calculate the acceleration due to gravity at a height of 300 km from the surface of the Earth. (M = 5.98 × 1024 kg, R = 6400 km).

Exercises | Q 4. (vii) | Page 99

Solve the following problem.

Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)

Exercises | Q 4. (viii) | Page 99

Solve the following problem.

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.

Exercises | Q 4. (ix) | Page 99

Solve the following problem.

A planet has mass 6.4 × 1024 kg and radius 3.4 × 106 m. Calculate the energy required to remove an object of mass 800 kg from the surface of the planet to infinity.

Exercises | Q 4. (x) | Page 99

Solve the following problem.

Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.

Exercises | Q 4. (xi) | Page 99

Solve the following problem.

A body weighs 5.6 kg-wt on the surface of the Earth. How much will be its weight on a planet whose mass is 1/7th mass of the Earth and radius twice that of the Earth’s radius?

Exercises | Q 4. (xii) | Page 99

Solve the following problem.

What is the gravitational potential due to the Earth at a point which is at a height of 2RE above the surface of the Earth?
(Mass of the Earth is 6 × 1024 kg, radius of the Earth = 6400 km and G = 6.67 × 10–11 N m2 kg–2)

Exercises

## Balbharati solutions for Physics 11th Standard Maharashtra State Board chapter 5 - Gravitation

Balbharati solutions for Physics 11th Standard Maharashtra State Board chapter 5 (Gravitation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Physics 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Physics 11th Standard Maharashtra State Board chapter 5 Gravitation are Introduction to Gravitation, Measurement of the Gravitational Constant (G), Variation in the Acceleration Due to Gravity with Altitude, Depth, Latitude and Shape, Gravitational Potential and Potential Energy, Earth Satellites, Kepler’s Laws, Newton’s Universal Law of Gravitation, Acceleration Due to Gravity (Earth’s Gravitational Acceleration).

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