The information in the table represents the effect of the mass of two objects on the gravitational force between the two objects.
| Mass of Object 1 (kg) | Mass of Object 2 (kg) | Distance between Objects 1 and 2 (m) | Gravitational Force between Objects 1 and 2 (N) |
|---|---|---|---|
| 1 | 1 | 1 | 4 |
| 2 | 1 | 1 | ? |
Which number should be in the cell with the question mark?
A. The number is two because when you double the mass of one of the objects, the force between the objects is halved.
B. The number is four because when you double the mass of one of the objects, the force between the objects remains the same.
C. The number is eight because when you double the mass of one of the objects, the force between the objects also doubles.
D. The number is sixteen because when you double the mass of one of the objects, the force between the objects increases by a factor of 4.
Answer (1)
The gravitational force is directly proportional to the product of the masses.
Doubling the mass of one object doubles the gravitational force.
The initial gravitational force is 4 N.
The new gravitational force is 2 × 4 = 8 N.
Explanation
Understanding the Problem Let's analyze the problem. We are given a table that shows the gravitational force between two objects with different masses. We need to find the gravitational force when the mass of one of the objects is doubled.
Gravitational Force and Mass The gravitational force between two objects is directly proportional to the product of their masses. This means that if we double the mass of one object, the gravitational force will also double, assuming the distance between the objects remains constant.
Applying the Concept In the first row of the table, the mass of Object 1 is 1 kg, the mass of Object 2 is 1 kg, and the gravitational force is 4 N. In the second row, the mass of Object 1 is 2 kg, the mass of Object 2 is 1 kg, and the distance is the same. Since the mass of Object 1 is doubled (from 1 kg to 2 kg), the gravitational force will also double.
Calculating the New Force Therefore, the gravitational force in the second row will be 2 × 4 = 8 N.
Final Answer The number that should be in the cell with the question mark is 8.
Examples
Imagine you're playing with magnets. If you have two magnets and they attract each other with a certain force, and then you double the strength of one magnet, the force between them will also double. This is similar to how gravity works between objects with mass. Understanding this relationship helps in designing spacecraft trajectories or predicting the motion of planets.
