If a person weighs 692 N on earth and 5320 N on the surface of a nearby planet, what is the acceleration due to gravity on that planet?

Approximately . (Approximately , where denotes the acceleration due to gravity on the surface of the earth.)

Explanation:

The weight of an object is the size of the overall gravitational pull on that object. If the mass of this person is , the weight of this person at a point with gravitational acceleration would be .

Let denote the gravitational acceleration on the surface of the earth. The weight of this person on the surface of the earth would be .

Let denote the gravitational acceleration on the surface of that "nearby planet". The weight of this person on the surface of that planet would be .

According to the question:

Take the quotient of these two equations:

.

.

.

In other words, the gravitational acceleration on the surface of that nearby planet is approximately times the gravitational acceleration on the surface of the earth.

The gravitational acceleration on the surface of the earth is approximately . Therefore, the gravitational acceleration on the surface of that planet would be approximately .