the radius of earth is 6000km what will be the weight of a 120 kg body if it is taken to a height of 2000km above the surface of earth?
To calculate the weight of a body at a different height above the surface of the Earth, we need to use the equation for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2),
m1 is the mass of Earth,
m2 is the mass of the body,
and r is the distance between the center of the Earth and the body.
Since the mass of the Earth and the body (120 kg) are constants, we can simplify the equation to:
F = (G * m2) / r^2
Now, we can calculate the weight of the body at a height of 2000 km:
Step 1: Convert the radius of the Earth and the height to meters:
Radius of Earth: 6000 km = 6000 * 1000 = 6,000,000 m
Height above Earth's surface: 2000 km = 2000 * 1000 = 2,000,000 m
Step 2: Calculate the distance between the body and the center of the Earth:
Distance (r) = Radius of Earth + Height above Earth's surface
Distance (r) = 6,000,000 m + 2,000,000 m = 8,000,000 m
Step 3: Calculate the gravitational force (weight):
F = (G * m2) / r^2
F = (6.674 × 10^-11 N(m/kg)^2 * 120 kg) / (8,000,000 m)^2
F = (6.674 × 10^-11 * 120) / (8,000,000)^2
Calculating the value of F will give us the weight of the body at a height of 2000 km above the surface of the Earth.
To find the weight of a body at a height above the Earth's surface, you need to consider the change in distance from the center of the Earth and use the formula for gravitational force.
Step 1: Find the gravitational force acting on the body at the Earth's surface (weight on the Earth's surface).
The gravitational force acting on a body is given by the formula: F = m * g, where F is the force (weight), m is the mass of the body, and g is the acceleration due to gravity.
The acceleration due to gravity at the Earth's surface is approximately 9.8 m/s^2. To convert this value to km/s^2, divide it by 1000, which gives 0.0098 km/s^2.
So, the weight at the Earth's surface is: weight = mass * acceleration due to gravity = 120 kg * 0.0098 km/s^2.
Step 2: Find the distance from the center of the Earth to the new height.
The radius of the Earth is given as 6000 km. To find the distance from the center of the Earth to a new height (2000 km above the surface), add the radius of the Earth to the height above the surface: 6000 km + 2000 km = 8000 km.
Step 3: Calculate the weight at the new height using the formula: weight = (mass * acceleration due to gravity) * (radius of the Earth / distance + radius of the Earth)^2.
Substituting the given values into the formula, we get: weight = (120 kg * 0.0098 km/s^2) * (6000 km / 8000 km)^2.
Simplifying further, weight = (120 * 0.0098) * (6000 / 8000)^2.
Finally, calculate the weight by multiplying the numbers together to get the answer.
use the gravitation formula
r is 8000km , find the mass of the Earth
the weight is the gravitational force times the mass of the body