Weight of a Body at Different Heights Above the Earth's Surface

Understanding Weight and Gravitational Force
Weight is the force experienced by an object due to the gravitational pull of the Earth. The weight of an object is determined by its mass and the acceleration due to gravity. The formula to calculate weight is:

Weight = Mass × Acceleration due to Gravity

The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s².

Calculating the Weight of a Body at a Height Above the Earth's Surface
To calculate the weight of a body at a height above the Earth's surface, we need to consider the change in distance from the center of the Earth. The weight of the body will decrease as it moves farther away from the Earth's surface.

Using the Radius of the Earth
Given that the radius of the Earth is 6000 km, we can calculate the distance from the center of the Earth to the height above its surface:

Distance from the center of the Earth = Radius of the Earth + Height above the surface

Distance from the center of the Earth = 6000 km + 2000 km = 8000 km

Calculating the Acceleration due to Gravity at the Given Height
To calculate the acceleration due to gravity at the given height, we can use the formula:

Acceleration due to Gravity = (Gravitational Constant × Mass of the Earth) / (Distance from the center of the Earth)²

The Gravitational Constant is approximately 6.67 × 10⁻¹¹ Nm²/kg², and the Mass of the Earth is approximately 5.97 × 10²⁴ kg.

Acceleration due to Gravity = (6.67 × 10⁻¹¹ Nm²/kg² × 5.97 × 10²⁴ kg) / (8000 km)²

Acceleration due to Gravity = 5.97 × 10²⁴ kg × 6.67 × 10⁻¹¹ Nm²/kg² / (8 × 10⁶ m)²

Acceleration due to Gravity ≈ 5.97 × 10²⁴ kg × 6.67 × 10⁻¹¹ Nm²/kg² / 6.4 × 10¹³ m²

Acceleration due to Gravity ≈ 5.97 × 6.67 / 6.4 × 10¹ m/s²

Acceleration due to Gravity ≈ 6.21 m/s²

Calculating the Weight of the Body at the Given Height
Now that we have the acceleration due to gravity at the given height, we can calculate the weight of the body using the formula:

Weight = Mass × Acceleration due to Gravity

Weight = 120 kg × 6.21 m/s²

Weight ≈ 745.2 N

Therefore, the weight of the 120 kg body at a height of 2000 km above the surface of the Earth is approximately 745.2 N.