Question

The free-fall acceleration at the surface of planet 1 is 18 {\rm {m/s}}^{2}. The radius and the mass of planet 2 are twice those of planet 1.

What is the free-fall acceleration on planet 2?
Express your answer using two significant figures.m/s^2.

Answer 1

Concepts and reason

The concepts used to solve this problem are free fall acceleration, Newton’s law of gravitation and Newton’s second law.

First find expression of free fall acceleration using Newton’s law of gravitation and Newton’s second law.

Then use the given condition that the radius and mass of planet 2 are twice those of planet 1 to find the free fall acceleration of planet 2.

Free falling object is an object that is falling under the influence of gravity. And a free falling object has acceleration in downward direction.

Fundamentals

From Newton’s law of gravitation, the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The expression for the Newton’s law of gravitation is,

Here, is the gravitational constant, is the mass of planet, is the mass of the object falling, is the force of attraction, and is the distance between the planet and the object.

From the Newton’s second law the acceleration of an object depends directly upon the net force acting on the object and inversely upon the mass of the object.

Then the expression for the acceleration of an object is,

Here, a is acceleration of an object and m is mass of object.

The expression for the Newton’s law of gravitation is,

The expression for the acceleration of an object is,

Substitute for F.

Therefore, the expression for the free fall acceleration is

The expression for the free fall acceleration of an object at the surface of planet 1 is,

…… (1)

Here, is free fall acceleration of an object at the surface of planet 1, is the mass of planet 1, and is the radius of the planet 1.

The expression for the free fall acceleration of an object at the surface of planet 2 is,

…… (2)

Here, is free fall acceleration of an object at the surface of planet 2, is the mass of planet 2, and is the radius of the planet 2.

The radius and mass of planet 2 are twice those of planet 1.

Substitute for and for in equation (2).

Substitute for .

Substitute for .

Therefore, the free fall acceleration of an object at the surface of planet 2 is .

Ans:

The free fall acceleration of an object at the surface of planet 2 is .