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Q33 PE

College Physics (Urone)
Found in: Page 191

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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/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.

(a) The calculated mass of the earth is M=5.979×1024kg

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

See the step by step solution

Step by Step Solution

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 103m

Gravitational acceleration near the North Pole = a = 9.83 m/s2

Earth’s mass = M = ?

The gravitational force is calculated as follows:

F = GMmR2

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=ma , here, is the object’s acceleration.

ma = GMmR2

M = aR2/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=5.979×1024kg 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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