Numerical Problem No. 5.9 (Gravitation) Physics SSC - I (Class 9)

A polar satellite is launched at 850 km above Earth. Find its orbital speed. Ans. (7431 ms⁻¹)

Given:  

Height of the Satellite  = h =  850 Km = = 0.85 ｘ 10³ｘ 10³ m = 0.85 ｘ 10⁶ m 

∴ Mass of the Earth = Mₑ = 6 ｘ 10²⁴ kg

∴ Radius of the Earth = Rₑ = 6.4 ｘ 10⁶ m

∴ Gravitational Constant = G = 6.67 ｘ 10⁻¹¹ N m² kg⁻²

To Find:

Orbital speed of Satellite = Vₒ = ? meters

Solution:   

We have the formula for the orbital speed of the Satellite

Vₒ = `\sqrt \frac {G Mₑ}{Rₑ + h}`

by putting the values we have

Vₒ = `\sqrt \frac {6.67 ｘ 10⁻¹¹ N m² kg⁻² ｘ 6 ｘ 10²⁴ kg}{6.4 ｘ 10⁶ m + 0.85 ｘ 10⁶ m }`

Vₒ = `\sqrt \frac {6.67 ｘ 6 ｘ 10⁻¹¹⁺²⁴ }{7.25 ｘ 10⁶}` m s⁻¹

Vₒ = `\sqrt \frac {6.67 ｘ 6 ｘ 10⁻¹¹⁺²⁴⁻⁶ }{7.25}`m s⁻¹

Vₒ = `\sqrt { 5.52 ｘ 10⁷ }`m s⁻¹

Vₒ = `\sqrt { 552 ｘ 10⁶ }`m s⁻¹

Vₒ = 0.742967ｘ 10³ m s⁻¹

or

Vₒ = 7429.67 m s⁻¹

or

Vₒ = 7430 m s⁻¹

Thus the orbital speed polar satellite will be 7430 ms⁻¹ when launched at 850 km above Earth. 

************************************

************************************

Shortcut Links For 

1. Physics 9th class main content List
2. Physics 9th class MCQs Quizzes All Units
3. Physics 10th class main content List
4. Physics 10th class MCQs Quizzes All Units

1. Website for School and College Level Physics   

(https://askrarequiz.blogspot.com)

2. Website for School and College Level Mathematics  

(https://askraremaths.blogspot.com)

3. Website for Single National Curriculum Pakistan - All Subjects Notes 

(https://askrareclassnotes.blogspot.com/)

© 2020-21 Academic Skills and Knowledge (ASK)     

Note:  Write me in the comments box below for any query and also Share this information with your class-fellows and friends.