Please give detailed solution for the given question: If the radius of earth decreases without changing the mass, would pendulum clocks placed at the surface of earth GAIN time?
Dear student,
Let's take an example,
If we consider the Earth to be a perfect sphere, then the acceleration due to gravity at its surface is given by .
Here, M is the mass of Earth; R is the radius of the Earth and G is universal gravitational constant.
If the radius of the earth is decreased by 1%, then the new radius becomes
New acceleration due to gravity will be given by
Hence, the value of the acceleration due to gravity increases when the radius is decreased.
Percentage increase in the acceleration due to gravity is given by
Let's take an example,
If we consider the Earth to be a perfect sphere, then the acceleration due to gravity at its surface is given by .
Here, M is the mass of Earth; R is the radius of the Earth and G is universal gravitational constant.
If the radius of the earth is decreased by 1%, then the new radius becomes
New acceleration due to gravity will be given by
Hence, the value of the acceleration due to gravity increases when the radius is decreased.
Percentage increase in the acceleration due to gravity is given by