Question

both the electrical force and the gravitational force between two objects share which relationship?
○ they are directly proportional to mass.
○ they are inversely proportional to the square of the distance.
○ they are inversely proportional to charge.
○ they are directly proportional to the square of the distance.

Explanation:

1. Recall the formulas:

• Gravitational force: $F_g = G\frac{m_1m_2}{r^2}$, where $G$ is gravitational constant, $m_1, m_2$ are masses, $r$ is distance.
• Electrical force (Coulomb's law): $F_e = k\frac{q_1q_2}{r^2}$, where $k$ is Coulomb's constant, $q_1, q_2$ are charges, $r$ is distance.

1. Analyze each option:

• Option 1: Electrical force depends on charge, not mass. Eliminate.
• Option 2: Both $F_g$ and $F_e$ have $1/r^2$ term, so they are inversely proportional to square of distance.
• Option 3: Gravitational force depends on mass, not charge. Eliminate.
• Option 4: Both have inverse relation with $r^2$, not direct. Eliminate.

Answer:

They are inversely proportional to the square of the distance.