If mass and radius of the Earth are 6.0×1024 kg and 6.4×106 m respectively, calculate the force exerted by the Earth on a body of mass 1 kg. Also, calculate acceleration produced in the body of mass 1 kg and acceleration produced in the Earth.
The accelerations of 1 kg mass and Earth are:
9.8 ms2 and 1.63×10−24 ms2 respectively
From Newton's law of gravitation, we know that the force of attaraction between the bodies is given by:
F = Gm1m2r2
Here, m1 = mass of Earth = 6.0×1024 kg and m2 = mass of the body = 1 kg
r = distance between the two bodies = radius of the Earth = 6.4×106 m
G = 6.67×10−11 Nm2kg2
F = 6.67×10−11×6.0×1024×1(6.4×106)2 = 9.8 N
This shows that Earth exerts a force of 9.8 N on a body of mass 1 kg. The body will exert an equal force of attraction of 9.8 N on the Earth.
Accelaration produced in the body of mass 1 kg:
Force = mass × acceleration
Therefore, Acceleration, a = Fm = F1 = 9.8 ms2
Thus, the acceleration produced in a body of mass 1 kg due to attraction of the Earth is 9.8 ms2, which is quite large. Thus, when a body is released, it falls towards the Earth with an acceleration of 9.8 ms2, which can be easily observed.
Acceleration produced in the Earth:
Similarly, acceleration of the Earth is given by ForceMass of Earth = 9.86.0×1024 = 1.63×10−24 ms2
This shows that the acceleration produced in the Earth by a body of mass 1 kg is 1.63×10−24 ms2 which is very small and cannot be observed.