Question

Calculate the gravitational acceleration at a distance twice the radius of the earth above the surface of the earth.​

Answer 1

Answer:

g =2.44262 m/s^2 ≈2.4m/s^2

Values:

Gravitational Constant'G' = 6.67 x 10^(-11) Nm^2/kg^2

Mass of earth'M' = 6 x 10^24kg

Radius of earth'r' = 6.4x10^6m

Twice radius of earth = 2 x 6.4x10^6m

=> '2r' = 12.8 x 10^6

Solution:

Since,

Gravitational Acceleration = GM/2r^2

=> g = GM/r^2

=> g = 6.67x10^(-11) Nm^2/kg^2 x 6 x 10^24kg / (12.8 x 10^6m)^2

=> g = 6.67x10^-11 x 6 x 10^24(kgm/s^2/kg^2xkg) / 163.84x10^12

=> g = 40.02x10^(24-11-12) m/s^2 / 163.84

=> g = (40.02 x 10^1 / 163.84) m/s^2

=> g = (400.2 / 163.84) m/s^2

=> g =2.44262 m/s^2

=> g ≈ 2.4 m/s^2

Thus, if the radius of earth is twice gravitational acceleration is 2.4 m/s^2.