Question

How does the weight of the body change (a) with latitude (b) with altitude (c) with the depth of the earth?

Accepted Answer

(a) With latitude:

The earth is not a perfect sphere. Its radius at the equator is longer than at the poles. The acceleration due to gravity $g$ of the earth is inversely proportional to the square of its radius at that point. Therefore, the value of $g$ at the poles is higher than that at the equator. The weight of a body of mass $m$ is given by,
$W = m \times g$
Therefore, the weight of a body is higher at the poles than at the equator.

(b) With altitude:

The weight of a body near the earth's surface is given by,
$W = m \times g$
The mass of the body $m$ remains the same everywhere. So, the weight of a body depends upon the value of $g$ at that place. The value of $g$ decreases with the height above the earth's surface. So, the weight of a body decreases with height (altitude). That is, a body would weigh less at higher altitudes than at the surface of the earth.

(c) With depth of the earth:

The weight of a body depends upon its mass $m$ and the acceleration due to gravity $g$ . The mass of a body does not change with its location. So, the weight of a body at any place depends upon the value of $g$ at that place.
The value of $g$ decreases as we go down inside the earth, and it becomes zero at the centre of the earth. So, the weight of a body decreases with the depth inside the earth and becomes zero at the centre of the earth.

Dr. S K Jain and Dr. Shailesh K Jain Solutions for Chapter: Gravitation, Exercise 4: Class Assignment 4

Dr. S K Jain Physics Solutions for Exercise - Dr. S K Jain and Dr. Shailesh K Jain Solutions for Chapter: Gravitation, Exercise 4: Class Assignment 4

Questions from Dr. S K Jain and Dr. Shailesh K Jain Solutions for Chapter: Gravitation, Exercise 4: Class Assignment 4 with Hints & Solutions

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