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Physics Part-I

Gravitation

A rocket is fired vertically with a speed of 5 kms^{-1} from t

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

Assume the earth to be a sphere of uniform mass density, how much would a body weigh (in N) half way down to the center of the earth if it weighed 250 N on the surface ?

A rocket is fired vertically with a speed of

5 km s^{- 1}

from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth

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

; mean radius of the radius of the Earth

= 6.4 \times 1 0^{6} m

;

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

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.

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Solving time: 3 mins

A rocket is fired vertically with a speed of $5 km s^{- 1}$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth $= 6.0 \times 1 0^{24} k g$ ; mean radius of the 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: Nov 16, 2023

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Physics Part-I (NCERT)

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Amelia Discussed

A rocket is fired vertically with a speed of

5 km s^{- 1}

from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth

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

; mean radius of the radius of the Earth

= 6.4 \times 1 0^{6} m

;

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

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Velocity of the rocket,

v = 5 \times 1 0^{3} m / s

Mass of the Earth,

M_{e} = 6 \times 1 0^{24} k g

Radius of the Earth,

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

Height reached by rocket mass

m = h

At the surface of the Earth,

Total energy of the rocket = Kinetic energy + Potential energy

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

At the highest point

h

v = 0 ⟹ Kinetic energy = 0

Potential energy = - \frac{G M _{e} m}{R _{e} + h}

Total energy of the rocket

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

By law of conservation of energy, total energy at surface = total energy at height h

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

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

Substituting

g = G M_{e} / R_{e}^{2}

and rearranging the terms,

h = \frac{R _{e} v ^{2}}{2 g R _{e} - v ^{2}}

= \frac{6.4 \times 1 0 ^{6} \times ( 5 \times 1 0 ^{3} ) ^{2}}{2 \times 9.8 \times 6.4 \times 1 0 ^{6} - ( 5 \times 1 0 ^{3} ) ^{2}}

= 1.6 \times 1 0^{6} m

Height achieved by the rocket with respect to the earth is

R_{e} + h = 6.4 \times 1 0^{6} + 1.6 \times 1 0^{6} = 8.01 0^{6} m

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Practice more questions from Physics Part-I (NCERT)

Assume the earth to be a sphere of uniform mass density, how much would a body weigh (in N) half way down to the center of the earth if it weighed 250 N on the surface ?

A rocket is fired vertically with a speed of

5 km s^{- 1}

from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth

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

; mean radius of the radius of the Earth

= 6.4 \times 1 0^{6} m

;

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

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.

View all

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Question Text	A rocket is fired vertically with a speed of $5 km s^{- 1}$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth $= 6.0 \times 1 0^{24} k g$ ; mean radius of the 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	Nov 16, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	584
Avg. Video Duration	7 min

Text solutionVerified

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A rocket is fired vertically with a speed of 5 kms−1 from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth =6.0×1024 kg; mean radius of the radius of the Earth =6.4×106 m; G=6.67×10−11 Nm2kg−2.

Text solutionVerified

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