#### Chapters

Chapter 2: Mathematical Methods

Chapter 3: Motion in a Plane

Chapter 4: Laws of Motion

Chapter 5: Gravitation

Chapter 6: Mechanical Properties of Solids

Chapter 7: Thermal Properties of Matter

Chapter 8: Sound

Chapter 9: Optics

Chapter 10: Electrostatics

Chapter 11: Electric Current Through Conductors

Chapter 12: Magnetism

Chapter 13: Electromagnetic Waves and Communication System

Chapter 14: Semiconductors

## Chapter 5: Gravitation

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

**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

**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

**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

**Choose the correct option.**

The binding energy of a satellite revolving around the planet in a circular orbit is 3 × 10^{9} J. It's kinetic energy is ______.

6 × 10

^{9}J–3 × 10

^{9}J–6 × 10

^{+9}J3 × 10

^{+9}J

**Answer the following question.**

State Kepler’s law of equal areas.

**Answer the following question.**

State Kepler’s law of the period.

**Answer the following question.**

What are the dimensions of the universal gravitational constant?

**Answer the following question.**

Define the binding energy of a satellite.

**Answer the following question.**

What do you mean by geostationary satellite?

**Answer the following question.**

State Newton’s law of gravitation.

**Answer the following question.**

Define the escape velocity of a satellite.

**Answer the following question.**

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

**Answer the following question.**

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

**Answer the following question.**

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

**Answer the following question.**

What is periodic time of a geostationary satellite?

**Answer the following question.**

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

**Answer the following question.**

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

**Answer the following question.**

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

**Answer the following question.**

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

**Answer the following question in detail.**

Derive an expression for the critical velocity of a satellite.

**Answer the following question in detail.**

State any four applications of a communication satellite.

**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`

**Answer the following question in detail.**

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

**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.

**Answer the following question in detail.**

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

**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.

**Answer the following question in detail.**

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

**Answer the following question in detail.**

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

**Answer the following question in detail.**

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

**Answer the following question.**

Define the binding energy of a satellite.

**Answer the following question in detail.**

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

**Answer the following question in detail.**

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

**Answer the following question in detail.**

State Kepler’s three laws of planetary motion.

**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.

**Answer the following question in detail.**

What is a critical velocity?

**Answer the following question in detail.**

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

**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`

**Answer the following question in detail.**

Define escape speed.

**Answer the following question in detail.**

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

**Answer the following question in detail.**

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

**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.

**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.

**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} Nm^{2}/kg^{2}

R = 6400 km, M = 6 × 10^{24} kg

**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 × 10^{4} km. Find radius of orbit of satellite A.

**Solve the following problem.**

Find the gravitational force between the Sun and the Earth.

Given Mass of the Sun = 1.99 × 10^{30} kg

Mass of the Earth = 5.98 × 10^{24} kg

The average distance between the Earth and the Sun = 1.5 × 10^{11} m.

**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 × 10^{24} kg, R = 6400 km).

**Solve the following problem.**

Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.

(M_{E} = 5.98 × 10^{24} kg, R = 6.4 × 10^{6} m)

**Solve the following problem.**

Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 10^{3} km and its mass is 6.4 × 10^{23} kg.

**Solve the following problem.**

A planet has mass 6.4 × 10^{24} kg and radius 3.4 × 10^{6} m. Calculate the energy required to remove an object of mass 800 kg from the surface of the planet to infinity.

**Solve the following problem.**

Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 10^{24} kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s^{2}.

**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 1/7^{th} mass of the Earth and radius twice that of the Earth’s radius?

**Solve the following problem.**

What 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 Earth is 6 × 10^{24} kg, radius of the Earth = 6400 km and G = 6.67 × 10^{–11} N m^{2} kg^{–2})

## Chapter 5: Gravitation

## 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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