If the earth acceleration due to gravity on a mass of 2000kg on the earth surface is 10ms.What will be the acceleration due to gravity when it is at a point twice the radius of the earth.What is the gravitational force on it.
F = G M1 M2/r^2
G, M1 and M2 are the same, only r changes
so in this problem
F = k/r^2
r2 = 2 r1
F1 = k/r1^1 = m g = 20,000N
F2 = k/r2^2 = k/4r1^2
F2/F1 = 1/4
F2 = 2000 * 10/4 = 5,000 N
F2 = m g2
5,000 = 2,000 g2
g2 = 2.5 m/s^2
To find the acceleration due to gravity at a point twice the radius of the Earth, we can use the formula for gravitational acceleration:
acceleration due to gravity (g2) = (G * M) / (r2^2)
Where:
- G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2)
- M is the mass of the Earth (approximately 5.97 x 10^24 kg)
- r2 is the distance from the center of the Earth to the point where the acceleration is being calculated.
In this case, twice the radius of the Earth is equal to 2 * (radius of the Earth). The radius of the Earth is approximately 6,371 kilometers or 6,371,000 meters.
So, the distance from the center of the Earth to the point of interest (r2) is 2 * 6,371,000 meters = 12,742,000 meters.
Now, plugging in the values into the formula:
g2 = (6.67 x 10^-11 N m^2/kg^2 * 5.97 x 10^24 kg) / (12,742,000 meters)^2
Simplifying the equation:
g2 = (3.98599 x 10^14 N) / (162,244,964,000,000 meters^2)
g2 ≈ 2.4652 m/s^2
Therefore, the acceleration due to gravity at a point twice the radius of the Earth is approximately 2.4652 m/s^2.
To calculate the gravitational force on a mass of 2000 kg at this point, we can use the formula:
Gravitational force (F) = mass (m) * acceleration due to gravity (g2)
F = 2000 kg * 2.4652 m/s^2
F ≈ 4,930.4 N
Therefore, the gravitational force on a mass of 2000 kg at a point twice the radius of the Earth is approximately 4930.4 Newtons.