Particles moving in a circle under their mutual gravitation

1. A.
   $\frac{\sqrt{(1 + 2\sqrt{2})G}}{2}$
2. B.
   $\sqrt{G(1 + 2\sqrt{2})}$
3. C.
   $\sqrt{\frac{G}{2}(2\sqrt{2} - 1)}$
4. D.
   $\sqrt{\frac{G}{2}(1 + 2\sqrt{2})}$

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1. A.
   $\sqrt{\frac{G}{2R^{3}}}$
2. B.
   $\frac{1}{2}\sqrt{\frac{G}{R^{3}}}$
3. C.
   $\frac{1}{2R}\sqrt{\frac{1}{G}}$
4. D.
   $\sqrt{\frac{2G}{R^{3}}}$

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1. A.
   $\frac{1}{2}\sqrt{\frac{GM}{R(2\sqrt{2} + 1)}}$
2. B.
   $\frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2} + 1)}$
3. C.
   $\frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2} - 1)}$
4. D.
   $\sqrt{\frac{GM}{R}}$

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1. A.
   $\sqrt{\frac{4Gm}{r}}$
2. B.
   $\sqrt{\frac{Gm}{4r}}$
3. C.
   $\sqrt{\frac{Gm}{r}}$
4. D.
   $\sqrt{\frac{Gm}{2r}}$

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1. A.
   $\sqrt{\frac{Gm}{2a^{3}}}$
2. B.
   $\sqrt{\frac{Gm}{8a^{3}}}$
3. C.
   $\sqrt{\frac{Gm}{4a^{3}}}$
4. D.
   $\sqrt{\frac{Gm}{a^{3}}}$

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