If the acceleration due to gravity is 9.8m/s^2 and
the radius of the earth is 6400km, calculate the mass of the earth,(G=6.7 × 10-11 Nm° kg-)
We can use the formula for the acceleration due to gravity to relate it to the mass of the Earth:
g = G * (m_Earth / r^2)
Where:
g = acceleration due to gravity (9.8 m/s^2)
G = gravitational constant (6.7 × 10^-11 Nm^2/kg^2)
m_Earth = mass of the Earth
r = radius of the Earth (6400 km = 6400 * 10^3 m)
Rearranging the equation to solve for m_Earth:
m_Earth = (g * r^2) / G
Substituting the given values:
m_Earth = (9.8 * (6400 * 10^3)^2) / (6.7 × 10^-11)
Calculating:
m_Earth = 5.972 × 10^24 kg
Therefore, the mass of the Earth is approximately 5.972 × 10^24 kg.
To calculate the mass of the Earth using the given information, we will use the formula for the acceleration due to gravity:
g = (G * M) / (R^2)
Where:
g = acceleration due to gravity = 9.8 m/s^2
G = gravitational constant = 6.7 × 10^-11 Nm^2/kg^2
M = mass of the Earth (what we are trying to find)
R = radius of the Earth = 6400 km = 6400 * 1000 m = 6,400,000 m
Rearranging the formula, we get:
M = (g * R^2) / G
Substituting the given values:
M = (9.8 m/s^2 * (6,400,000 m)^2) / (6.7 × 10^-11 Nm^2/kg^2)
Calculating the above expression will give us the mass of the Earth.