Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 768

A small satellite is revolving near earth's surface. Its orbital velocity will be nearly \(=\ldots \ldots \ldots \ldots \mathrm{kms}^{-1}\). (A) 8 (B) 4 (C) 6 (D) \(11.2\)

Short Answer

Expert verified
The orbital velocity of a small satellite revolving near the Earth's surface is approximately 8 \(\mathrm{km/s}\).

Step by step solution

01

Write the formula for orbital velocity

Orbital velocity (V) is the velocity an object requires to stay in a stable orbit around another celestial body, like a planet or a moon. The formula for orbital velocity is given by: \[V = \sqrt{\frac{GM}{R}}\] Where: - V is the orbital velocity - G is the gravitational constant (\(6.67 \times 10^{-11} \mathrm{N} \cdot \mathrm{m}^2 \cdot \mathrm{kg}^{-2}\)) - M is the mass of the celestial body (in this case, Earth's mass, which is \(5.97 \times 10^{24} \mathrm{kg}\)) - R is the distance from the center of the celestial body to the object in orbit (in this case, Earth's radius, which is approximately \(6.37 \times 10^6 \mathrm{m}\))
02

Substitute values and calculate the orbital velocity

We'll now substitute the given values for G, M, and R into the orbital velocity formula: \[V = \sqrt{\frac{(6.67 \times 10^{-11} \mathrm{N} \cdot \mathrm{m}^2 \cdot \mathrm{kg}^{-2})(5.97 \times 10^{24} \mathrm{kg})}{(6.37 \times 10^6 \mathrm{m})}}\] Now we'll solve for V: \[V \approx 7.9 \times 10^3 \mathrm{m/s}\]
03

Convert the orbital velocity to \(\mathrm{km/s}\) and select the correct answer

Wrap up the process by converting the orbital velocity from \(\mathrm{m/s}\) to \(\mathrm{km/s}\) as requested: \[V \approx 7.9 \times 10^3 \mathrm{m/s} \times (\frac{1 \mathrm{km}}{1000 \mathrm{m}}) \approx 7.9 \mathrm{km/s}\] Looking at the given choices, the closest option to our calculated orbital velocity of \(7.9 \mathrm{km/s}\) is choice (A) 8 \(\mathrm{km/s}\). So, the correct answer is: (A) 8 \(\mathrm{km/s}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The maximum and minimum distance of a comet from the sun are $8 \times 10^{12} \mathrm{~m}\( and \)1.6 \times 10^{12} \mathrm{~m} .$ If its velocity when nearest to the sun is \(60 \mathrm{~ms}^{-1}\), What will be its velocity in \(\mathrm{ms}^{-1}\) when it is farthest? (A) 6 (B) 12 (C) 60 (D) 112

A geo-stationary satellite is orbiting the earth of a height of \(6 \mathrm{R}\) above the surface of earth, \(\mathrm{R}\) being the radius of earth. The time period of another satellite at a height of \(2.5 \mathrm{R}\) from the surface for earth is \(=\ldots \ldots \ldots \ldots\) (A) 6 (B) \(6 \sqrt{2}\) (C) 10 (D) \(6 / \sqrt{2}\)

A body of mass \(\mathrm{m}\) is taken from earth surface to the height \(\mathrm{h}\) equal to radius of earth, the increase in potential energy will be (A) \(\operatorname{mg} R\) (B) \((1 / 2) \mathrm{mgR}\) (C) \(2 \mathrm{mg} \mathrm{R}\) (D) \((1 / 4) \mathrm{mgR}\)

The escape velocity for a sphere of mass \(\mathrm{m}\) from earth having mass \(\mathrm{M}\) and Radius \(\mathrm{R}\) mass is given by (A) \(\sqrt{[}(2 \mathrm{GM}) / \mathrm{R}]\) (B) \(2 \sqrt{(\mathrm{GM} / \mathrm{R})}\) (C) \(\sqrt{[}(2 \mathrm{GMm}) / \mathrm{R}]\) (D) \(\sqrt{(\mathrm{GM} / \mathrm{R})}\)

The escape velocity of a projectile from the earth is approximately (A) \(11.2 \mathrm{kms}^{-1}\) (B) \(112 \mathrm{kms}^{-1}\) (C) \(11.2 \mathrm{~ms}^{-1}\) (D) \(1120 \mathrm{kms}^{-1}\)
See all solutions

Recommended explanations on English Textbooks

Graphology

Read Explanation

Essay Writing Skills

Read Explanation

Summary Text

Read Explanation

Essay Prompts

Read Explanation

English Grammar Summary

Read Explanation

Argumentative Essay

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free