Question

What is the gravitational force between two 5 kg masses placed 2 meters apart? (Take \( G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \))

• A. \( 4.17 \times 10^{-10} \, \text{N} \)
• B. \( 8.34 \times 10^{-10} \, \text{N} \)
• C. \( 1.67 \times 10^{-10} \, \text{N} \)
• D. \( 2.50 \times 10^{-11} \, \text{N} \)

Hint:

Gravitational force is extremely weak unless very massive bodies are involved. Always use \( F = \frac{Gm_1m_2}{r^2} \) and keep track of units.

Answer 1

The Correct Option is B

Use Newton's law of universal gravitation: \[ F = \frac{G m_1 m_2}{r^2} \] Given: \( m_1 = m_2 = 5 \, \text{kg} \), \( r = 2 \, \text{m} \), \( G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \) \[ F = \frac{6.67 \times 10^{-11} \times 5 \times 5}{2^2} = \frac{6.67 \times 25 \times 10^{-11}}{4} \] \[ F = \frac{166.75 \times 10^{-11}}{4} = 41.6875 \times 10^{-11} = 8.34 \times 10^{-10} \, \text{N} \] Option (b) is correct.