Suppose that the mass of the Earth has become 2 times, and the radius is 1.2 times more

| May 4, 2021 | education

Suppose that the mass of the Earth has become 2 times, and the radius is 1.2 times more. Determine how many times the gravity force acting on the body at the pole has changed.

The path the mass of the body at the pole will be m. Then the force of gravity will be equal to:

F = G * m * M / R ^ 2 where:

G – gravitational constant;

M is the mass of the Earth;

R is the radius of the Earth.

According to the condition of the problem, the mass of the Earth has increased by 2 times, and the radius by 1.2 times. Then the force of gravity will be equal to:

F1 = G * 2 * m * M / (1.2 * R) ^ 2 = 2 * G * m * M / 1.44 / R ^ 2.

Dividing F1 by F, we get:

F1 / F = (2 * G * m * M * R ^ 2) / (1.44 * R ^ 2 * G * m * M) = 2 / 1.44 = 1.4.

Answer: the force of gravity will be 1.4 times greater.



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