Four particles, each of mass

Question:

Four particles, each of mass $\mathrm{M}$ and equidistant from each other, move along a circle of radius $\mathrm{R}$ under the action of their mutual gravitational attraction. The speed of each particle is :

  1. $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}(1+2 \sqrt{2})}$

  2. $\frac{1}{2} \sqrt{\frac{\mathrm{GM}}{\mathrm{R}}(1+2 \sqrt{2})}$

  3. $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$

  4. $\sqrt{2 \sqrt{2} \frac{\mathrm{GM}}{\mathrm{R}}}$


Correct Option: , 2

Solution:

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