Question

Two charged objects with mass are initially 1 meter apart. If we increase the mass of each object by 2x, which of the following statements are true?

1. The electrostatic force between the two objects decreases by 4x.
2. The gravitational force between the two objects increases by 2x.
3. The gravitational force between the two objects decreases by 4x.
4. The electrostatic force between the two objects increases by 2x.
Options:

A. 1 only
B. 2 only
C. 3 only
D. 4 only
E. 1 and 3
F. 2 and 4
G. 1, 2, and 3
H. 1, 3, and 4
I. 2, 3, and 4

Answer 1

Doubling the mass of two objects does not change the electrostatic force but increases the gravitational force by a factor of 4x.

Step-by-step explanation:

When examining the effects of increasing the mass of two charged objects on the electrostatic and gravitational forces between them, we must consider Coulomb's Law for electrostatic forces and Newton's Law of Universal Gravitation for gravitational forces.

According to Coulomb's Law, the electrostatic force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Increasing the mass does not change the charges of the objects, so the electrostatic force remains unchanged, refuting options 1 and 4.

According to Newton's Law of Universal Gravitation, the gravitational force between two masses is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. If each object's mass is increased by 2x, the gravitational force increases by the factor of (2x * 2x) = 4x, confirming option 2 and refuting option 3.

Hence, the correct answer for the impact of doubling the mass on the forces is that the gravitational force between the objects increases by 4x, which agrees with option B: 2 only.