Consider a spherical volume of space that is large enough to be considered homogeneous. Also consider a particle on the surface of this volume that is moving away from the center with the Hubble flow. Assuming that the pressure within the volume is negligible, the universe will re-collapse if the particle's Hubble speed is: A. Greater than its escape speed from the mass within the volume B. The same as its escape speed from the mass within the volume C. Less than its escape speed from the mass within the volume

Option A applies.

A.  Greater than its escape speed from the mass within the volume

Explanation:

Here it is mentioned that the spherical volume is large enough for the space to be considered as homogeneous. Also, the pressure within the volume is negligible, so that will not result into the re collapse of the Universe. Now as per our knowing, Hubble's Law relates the average speed of the particle to the distance R between the Earth and the particle. So, if the particle's speed is greater than it's escape speed from the mass within the volume, then the Universe is bound to re collapse back again. Option A applies.