Question

In the given situation, the force at the center on 1 kg mass is \( F_1 \). Now if \( 4m \) and \( 3m \) are interchanged, the force is \( F_2 \). Given \( \frac{F_1}{F_2} = \frac{2}{\sqrt{\alpha}} \), find \( \alpha \).

• A. \( \alpha = 5 \)
• B. \( \alpha = 3 \)
• C. \( \alpha = 7 \)
• D. \( \alpha = 1 \)

Hint:

When forces depend on distance, changing the distance between masses can significantly affect the force, which is inversely proportional to the square of the distance.

Answer 1

The Correct Option is A

Step 1: Use the formula for forces.
The force between two masses \( F = G \frac{m_1 m_2}{r^2} \), where \( r \) is the distance between the masses. In this case, the change in distance will affect the force. Step 2: Apply the given relation.
The relationship \( \frac{F_1}{F_2} = \frac{2}{\sqrt{\alpha}} \) is used to find \( \alpha \), considering the new distance after interchanging \( 4m \) and \( 3m \). Step 3: Conclusion.
Solving the equation, we find that \( \alpha = 5 \). Final Answer: \[ \boxed{\alpha = 5} \]