A small particle is thrown parallel to the earth’s surface with initial velocity $\mathrm{\mu }$ wrt earth assuming there is no other planet and that the velocity of the earth is zero, then which of the following will be correct

For the particle to move in circular orbit around the earth minimum value of ‘$\mathrm{\mu }$’ must be $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$

For the particle to escape, minimum u should be equal to $\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}$

For particle to escape, minimum  u should be more than$\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}$

The total mechanical energy of the particle and the earth system remain conserved