Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

(a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is ${9.830 m/s}^{2}$ and the radius of the Earth is $6371 k m$ from pole to pole. (b) Compare this with the accepted value of $M = 5.979 \times 10^{24} k g$ .

(a) The calculated mass of the earth is $M = 5.979 \times 10^{24} k g$

(b) The calculated value is matching with accepted value.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of Gravity

Gravity is a universal phenomenon and is introduced by Newton and Derived the expression for gravitational force.

Step 2: Calculating the mass of Earth

Earth’s radius ${= R = 6371 x 10}^{3} m$

Gravitational acceleration near the North Pole ${= a = 9.83 m/s}^{2}$

Earth’s mass $= M = ?$

The gravitational force is calculated as follows:

$F = G \frac{Mm}{R^{2}}$

Here, $m$ is object’s mass, $M$ is Earth’s mass, R Earth’s radius is the gravitation constant and F is the gravitational force. The force acting on the object is calculated as follows: $F = m a$ , here, is the object’s acceleration.

$ma = G \frac{Mm}{R^{2}}$

${M = aR}^{2} /G$

$M = (9.83 \times {(6371 \times 10^{3})}^{2}) / (6.637 \times 10^{- 11})$

$M = 5.979 \times 10^{24} k g$

This is the calculated mass of the earth.

Step 3: Determining difference between the calculated and accepted value

The calculated value of mass is $M = 5.979 \times 10^{24} k g$ which is exactly matching with the accepted value of the mass of the earth. The difference in percent between the computed and approved values is zero percent.

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is ${9.830 m/s}^{2}$ and the radius of the Earth is $6371 k m$ from pole to pole. (b) Compare this with the accepted value of $M = 5.979 \times 10^{24} k g$ .

Step by Step Solution

Step 1: Definition of Gravity

Step 2: Calculating the mass of Earth

Step 3: Determining difference between the calculated and accepted value

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is 9.830 m/s2 and the radius of the Earth is 6371km from pole to pole. (b) Compare this with the accepted value of M=5.979×1024kg.

Step by Step Solution

Step 1: Definition of Gravity

Step 2: Calculating the mass of Earth

Step 3: Determining difference between the calculated and accepted value

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(a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is ${9.830 m/s}^{2}$ and the radius of the Earth is $6371 k m$ from pole to pole. (b) Compare this with the accepted value of $M = 5.979 \times 10^{24} k g$ .