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Physics Part-I

Gravitation

A satellite orbits the earth at a height of 400 km above the s

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

16 questions

Chapter 2: Units and Measurements

51 questions

Chapter 3: Motion in Straight Line

50 questions

Chapter 4: Motion in a Plane

43 questions

Chapter 5: Laws of motion

52 questions

Chapter 6: Work, Energy and Power

41 questions

Chapter 7: System of Particles and Rotational Motion

45 questions

Chapter 8: Gravitation

33 questions

The escape speed of a projectile on the earth's surface is

11.2 km s^{- 1}

. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite

= 200 k g

; mass of the earth

= 6.0 \times 1 0^{24} k g

; radius of the earth

= 6.4 \times 1 0^{6} m

; G =

6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

Two stars each of one solar mass

(= 2 \times 1 0^{30} k g)

are approaching each other for a head on collision. When they are a distance

1 0^{9} km

, their speeds are negligible. What is the speed with which they collide ? The radius of each star is

1 0^{4} km

. Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Question

Easy

Solving time: 1 mins

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $= 200 k g$ ; mass of the earth $= 6.0 \times 1 0^{24} k g$ ; radius of the earth $= 6.4 \times 1 0^{6} m$ ; G = $6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$ .

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Updated on: Jun 7, 2022

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Physics Part-I (NCERT)

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Evelyn Discussed

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite

= 200 k g

; mass of the earth

= 6.0 \times 1 0^{24} k g

; radius of the earth

= 6.4 \times 1 0^{6} m

; G =

6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Mass of the Earth,

M = 6.0 \times 1 0^{24} k g

m = 200 k g

R_{e} = 6.4 \times 1 0^{6} m

G = 6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

Height of the satellite,

h = 400 km = 4 \times 1 0^{5} m

Total energy of the satellite at height h

= (1/2) m v^{2} + (- G \frac{M _{e} m}{( R _{e} + h )})

Orbital velocity of the satellite,

v = \frac{G M _{e}}{R _{e} + h}

Total energy at height h

= \frac{1}{2} \frac{G M _{e} m}{R _{e} + h} - \frac{G M _{e} m}{R _{e} + h}

T o t a l E n er g y = - \frac{1}{2} \frac{G M _{e} m}{R _{e} + h}

The negative sign indicates that the satellite is bound to the Earth.

Energy required to send the satellite out of its orbit = – (Bound energy)

= \frac{G M _{e} m}{2 ( R _{e} + h )}

= \frac{6.67 \times 1 0 ^{- 11} \times 6 \times 1 0 ^{24} \times 200}{2 ( 6.4 \times 1 0 ^{6} + 4 \times 1 0 ^{5} )}

= 5.9 \times 1 0^{9} J

If the satellite just escapes from the gravitational field, then total energy of the satellite is zero. Therefore, we have to supply

5.9 \times 1 0^{9} J

of energy to just escape it.

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Practice more questions from Physics Part-I (NCERT)

The escape speed of a projectile on the earth's surface is

11.2 km s^{- 1}

. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite

= 200 k g

; mass of the earth

= 6.0 \times 1 0^{24} k g

; radius of the earth

= 6.4 \times 1 0^{6} m

; G =

6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

Two stars each of one solar mass

(= 2 \times 1 0^{30} k g)

are approaching each other for a head on collision. When they are a distance

1 0^{9} km

, their speeds are negligible. What is the speed with which they collide ? The radius of each star is

1 0^{4} km

. Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Question Text	A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite $= 200 k g$ ; mass of the earth $= 6.0 \times 1 0^{24} k g$ ; radius of the earth $= 6.4 \times 1 0^{6} m$ ; G = $6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$ .
Updated On	Jun 7, 2022
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	309
Avg. Video Duration	8 min

Text solutionVerified

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