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

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

The gravitational force is calculated using the formula: \( F = \dfrac{G \cdot m_1 \cdot m_2}{r^2} \)

With the provided values, the calculation is: \( F = \dfrac{6.67 \times 10^{-11} \cdot 10 \cdot 20}{5^2} \) which simplifies to \( F = \dfrac{6.67 \times 10^{-11} \cdot 200}{25} \). This further reduces to \( F = \dfrac{1.334 \times 10^{-8}}{25} \), resulting in a force of \( 5.336 \times 10^{-10} \, \text{N} \).

Correct Answer:

Option 1: \( 5.33 \times 10^{-10} \, \text{N} \)