Question

Two bodies of masses \( m_1 = 5 \, \text{kg} \) and \( m_2 = 10 \, \text{kg} \) are placed 2 meters apart. What is the gravitational force between them?

• A. \( 8.34 \times 10^{-10} \, \text{N} \)
• B. \( 6.67 \times 10^{-11} \, \text{N} \)
• C. \( 3.34 \times 10^{-7} \, \text{N} \)
• D. \( 2.00 \times 10^{-10} \, \text{N} \)

Hint:

To calculate the gravitational force between two masses, use the formula \( F = G \frac{m_1 m_2}{r^2} \) and ensure to use the correct value for the gravitational constant.

Answer 1

The Correct Option is A

Given:

• Mass of body 1: \( m_1 = 5 \, \text{kg} \)
• Mass of body 2: \( m_2 = 10 \, \text{kg} \)
• Distance between them: \( r = 2 \, \text{m} \)

Step 1: Use the Gravitational Force Formula

The formula for the gravitational force between two masses is:

\[ F = G \frac{m_1 m_2}{r^2} \] where: - \( F \) is the gravitational force, - \( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \) is the gravitational constant, - \( m_1 \) and \( m_2 \) are the masses, - \( r \) is the distance between the masses.

Step 2: Substitute the values into the formula

\[ F = (6.67 \times 10^{-11}) \frac{(5)(10)}{(2)^2} \] \[ F = (6.67 \times 10^{-11}) \times \frac{50}{4} \] \[ F = (6.67 \times 10^{-11}) \times 12.5 = 8.3375 \times 10^{-10} \, \text{N} \]

Step 3: Round to appropriate significant figures

\[ F \approx 8.34 \times 10^{-10} \, \text{N} \]

✅ Final Answer:

The gravitational force between the two bodies is approximately \( \boxed{8.34 \times 10^{-10} \, \text{N}} \).