Question

a ball is moved from earth to a planet that has a gravitational acceleration that is double that of earth. How does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball and when it is on earth

Answer 1

Answer:

The gravitational force of the ball on the new planet will be double the gravitational force of the ball on Earth

Explanation:

The force of one body of mass M on another of mass m, is given from Newton's law of gravitation as the product of the acceleration due to gravity of the body and the mass of the other body as follows;

$F =\dfrac{G \times M}{R^{2}} \times m$

Where;

$\dfrac{G \times M}{R^{2}} = g = The\ acceleration \ due \ to \ gravity$

Therefore, when the acceleration due to gravity is doubled, the gravitational force also doubles

Answer 2

The gravitational force becomes double on doubling the gravitational acceleration.

The given problem is based on the concept of Gravitational force. The force of one body of mass M on another of mass m, is given from Newton's law of gravitation as the product of the acceleration due to gravity of the body and the mass of the other body as follows;

$F=\dfrac{G \times M \times m}{R^{2}}$

Here, G is the universal gravitational constant.

And, the expression is also written as,

$F=g \times m$

Where, $g=\dfrac{G \times M}{R^{2}}$  is called gravitational acceleration.

So clearly the gravitational acceleration is directly proportional to force due to gravitation. Therefore on increasing the gravitational acceleration twice, the gravitational force also increases twice.

Thus, we can conclude that the gravitational force doubles on doubling the gravitational acceleration.

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