Question

What is the gravitational force between two objects of masses \( m_1 = 10 \, \text{kg} \) and \( m_2 = 20 \, \text{kg} \), separated by a distance of \( r = 5 \, \text{m} \)? (Gravitational constant \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \))

• A. \( 1.33 \times 10^{-9} \, \text{N} \)
• B. \( 2.67 \times 10^{-9} \, \text{N} \)
• C. \( 4.67 \times 10^{-9} \, \text{N} \)
• D. \( 5.33 \times 10^{-9} \, \text{N} \)

Hint:

Remember: Gravitational force decreases with the square of the distance between the objects, as described by \( F = \frac{G m_1 m_2}{r^2} \).

Answer 1

The Correct Option is A

Step 1: Use the formula for gravitational force \[ F = \frac{G m_1 m_2}{r^2} \] Given: - \( m_1 = 10 \, \text{kg} \) - \( m_2 = 20 \, \text{kg} \) - \( r = 5 \, \text{m} \) - \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \) Substitute the values into the formula: \[ F = \frac{(6.67 \times 10^{-11}) \times 10 \times 20}{(5)^2} = \frac{1.334 \times 10^{-9}}{25} = 1.33 \times 10^{-9} \, \text{N} \] Answer: Therefore, the gravitational force between the two objects is \( 1.33 \times 10^{-9} \, \text{N} \). So, the correct answer is option (1).