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Two identical thin rings each of radius \( R \) are coaxially placed at a distance \( R \). If the rings have a uniform mass
\( P \) distribution and each has mass \( m_{1} \) and \( m_{2} \) respectively, then

W the work done in moving a mass \( m \) from centre of one ring to that of the other is :
(A) Zero
(B) \( \frac{G m\left(m_{1}-m_{2}\right)(\sqrt{2}-1)}{\sqrt{2} R} \)
(C) \( \frac{G m \sqrt{2}\left(m_{1}+m_{2}\right)}{R} \)
(D) \( \frac{G m m_{1}(\sqrt{2}+1)}{m_{2} R} \)
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