Final answer:
Reducing the distance between two masses by half will result in the greatest increase in gravitational force, according to the law of universal gravitation, because the force increases as the squared inverse of the distance. This option multiplies the force by a factor of four.
Step-by-step explanation:
To determine which of the given options will result in the greatest increase in the gravitational force between two objects with different masses, we must use the law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses (m1*m2) and inversely proportional to the square of the distance (r2) between them.
Now let's evaluate the options:
- Reducing the small mass by half does not increase the gravitational force; it actually decreases it.
- Reducing the distance between the masses by half increases the gravitational force by a factor of four (since (1/2)2 = 1/4, and the inverse is 4).
- Doubling the distance between the two masses reduces the gravitational force by a factor of four, not an increase.
- Doubling the amount of the large mass doubles the gravitational force, which is a significant increase but not as much as reducing the distance by half.
The option that results in the greatest increase is therefore b. Reducing the distance between the masses by half.