Weight of a body at a height equal to the radius of the Earth

To understand the weight of a body at a height equal to the radius of the Earth, we need to consider the gravitational force acting on the body. The weight of an object is the force with which it is pulled towards the center of the Earth due to gravity.

At the surface of the Earth, the weight of a body can be calculated using the formula:

Weight = mass x gravitational acceleration

- The weight of an object at the surface of the Earth is denoted by N, which represents the force acting on the body due to gravity.

Weight at a height equal to 3 times the radius of the Earth

To determine the weight of the body at a height equal to three times the radius of the Earth, we need to consider the change in gravitational acceleration.

- Gravitational acceleration decreases with an increase in height from the surface of the Earth.
- As we move away from the Earth's surface, the distance between the center of the Earth and the body increases, resulting in a decrease in the gravitational force.

Explanation

1. Weight and gravitational force
- Weight is the force with which an object is pulled towards the center of the Earth.
- The gravitational force is responsible for this weight, and it is directly proportional to the mass of the object.
- The weight can be calculated by multiplying the mass of the object by the gravitational acceleration.

2. Gravitational acceleration
- Gravitational acceleration is the acceleration due to gravity near the surface of the Earth.
- It is denoted by 'g' and has a constant value of approximately 9.8 m/s^2.
- Gravitational acceleration decreases with an increase in height from the surface of the Earth.
- This decrease is due to the inverse square law, which states that the gravitational force decreases by the square of the distance.

3. Weight at a height equal to 3 times the radius of the Earth
- When we move to a height equal to three times the radius of the Earth, the distance from the center of the Earth increases.
- As the distance increases, the gravitational force decreases.
- Using the inverse square law, we can calculate the new gravitational acceleration at this height.
- Once we have the new gravitational acceleration, we can calculate the weight of the body using the formula: Weight = mass x gravitational acceleration.

Conclusion

In conclusion, the weight of a body at a height equal to three times the radius of the Earth will be less than its weight at the surface of the Earth. This is because the gravitational force decreases with an increase in height. It is important to consider the inverse square law and the change in gravitational acceleration when calculating the weight at different heights.