  It has been argued that the low-mass primordial stars ($m_{\rm Pop III}\,\leq
0.8\,M_\odot$) are likely to enter the main sequence and hence possibly be
found in the present-day Galaxy. However, due to limitations in existing
numerical capabilities, current three-dimensional (3D) simulations of disk
fragmentation are capable of following only a few thousands of years of
evolution after the formation of the first protostar. In this work we use a
modified version of {\sc Gadget}-2 smoothed particle hydrodynamics(SPH) code to
present the results of non-linear collapse of the gas clouds associated with
various degrees of initial solid body rotation (parameterized by $\beta$) using
a piecewise polytropic equation of state. The 3D simulations are followed till
the epoch when 50$M_{\odot}$ of mass has been accreted in protostellar objects,
which is adequate enough to investigate the dynamics of the protostars with the
surrounding gaseous medium and to determine the mass function, accretion rate
and survival possibility of these protostellar objects till present epoch. We
found that evolving protostars that stay within slow-rotating parent clouds can
become massive enough due to accretion in the absence of radiative feedback,
whereas $10-20 \%$ of those formed within a fast-rotating clouds ($\beta \ge
0.1$) have the possibility to get ejected from the gravitational bound cluster
as low mass stars.
