Weight and Gravity

Weight is the force exerted on an object due to gravity. It is directly proportional to the mass of the object and the acceleration due to gravity. The weight of an object can vary depending on the distance from the center of the Earth.

Acceleration due to Gravity

The acceleration due to gravity, denoted by g, is the rate at which an object falls towards the Earth under the influence of gravity. It is approximately 9.8 m/s² on the surface of the Earth. The acceleration due to gravity decreases as we move away from the surface of the Earth.

Height and Weight

When an object is taken to a height above the surface of the Earth, the distance between the object and the center of the Earth increases. As a result, the acceleration due to gravity decreases, leading to a decrease in weight.

Calculating the Percentage Decrease

To calculate the percentage decrease in weight when taken to a height of 32 km above the surface of the Earth, we need to compare the weights at the two locations.

Step 1: Calculate the weight at the surface of the Earth:
The weight at the surface of the Earth can be calculated using the formula:
Weight = mass × acceleration due to gravity

Step 2: Calculate the weight at a height of 32 km above the surface of the Earth:
To calculate the weight at this height, we need to use the radius of the Earth and the height to find the distance from the center of the Earth. Let's denote this distance as "d".
d = radius of the Earth + height above the surface
Using the given radius of the Earth as 6400 km and the height of 32 km, we can calculate the new distance from the center of the Earth.

Step 3: Calculate the new acceleration due to gravity at this height:
The acceleration due to gravity can be calculated using the formula:
g' = (g × (radius of the Earth)²) / (d)²

Step 4: Calculate the new weight at this height:
The weight at this height can be calculated using the formula:
Weight' = mass × g'

Step 5: Calculate the percentage decrease in weight:
Percentage decrease = ((Weight - Weight') / Weight) × 100

Summary:
To find the percentage decrease in weight when taken to a height of 32 km above the surface of the Earth, we need to calculate the weight at the surface of the Earth and at the given height. By comparing the two weights, we can determine the percentage decrease.