Two hypothetical planets of masses \(m_1\) and \(m_2\) are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres . What is their speed when their separation is \('d'\) ? (Speed of \(m_1\) is \(v_1\) and that of \(m_2\) is \(v_2\) )

1. A \(v_1 = v_2\)
2. B \(\begin{array}{l}
   {v_1}{\mkern 1mu}  = {\mkern 1mu} {m_2}{\mkern 1mu} \sqrt {\frac{{2G}}{{d({m_1} + {m_2})}}} \\
   {v_2}{\mkern 1mu}  = {\mkern 1mu} {m_1}{\mkern 1mu} \sqrt {\frac{{2G}}{{d({m_1} + {m_2})}}} 
   \end{array}\)
3. C \(\begin{array}{l}
   {v_1}{\mkern 1mu}  = {\mkern 1mu} {m_1}{\mkern 1mu} \sqrt {\frac{{2G}}{{d({m_1} + {m_2})}}} \\
   {v_2}{\mkern 1mu}  = {\mkern 1mu} {m_2}{\mkern 1mu} \sqrt {\frac{{2G}}{{d({m_1} + {m_2})}}} 
   \end{array}\)
4. D \(\begin{array}{l}
   {v_1}\, = \,{m_2}\,\sqrt {\frac{{2G}}{{{m_1}}}} \\
   {v_2}\, = \,{m_2}\,\sqrt {\frac{{2G}}{{{m_2}}}} 
   \end{array}\)