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Physics · GRAVITATION

हिन्दी

Four point masses, each of mass \( m \), are fixed at the corners of a square of side \( l \). What is the minimum work required to slowly move an additional test mass \( m_0 \) from infinity to the center of the square?

  1. \( 4\sqrt{2} \frac{G m m_0}{l} \)
  2. \( 2\sqrt{2} \frac{G m m_0}{l} \)
  3. \( -4\sqrt{2} \frac{G m m_0}{l} \)
  4. \( -2\sqrt{2} \frac{G m m_0}{l} \)

Correct answer · Option 3

\( -4\sqrt{2} \frac{G m m_0}{l} \)

Explanation

Gravitational potential at the center is \( V = -4 \frac{Gm}{l/\sqrt{2}} = -4\sqrt{2}\frac{Gm}{l} \). Work done by external agent is \( W_{\text{ext}} = m_0 (V - 0) = -4\sqrt{2}\frac{G m m_0}{l} \).
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