  Gravitational collapse of a spherically symmetric homogeneous perfect
barotropic fluid with linear as well as polytropic type Equation of State (EoS)
has been investigated in the framework of a linear model of $f(R,T)$ gravity.
This modified gravity has the potential to explain the observed cosmic
acceleration. The calculations have been done taking the transformed time
coordinate $t \to \sqrt{\frac{\rho_0}{3}} t$, where $\rho_0$ is the initial
density of the fluid. For linear EoS $p=\omega\rho$, the condition for being a
true singularity, along with sufficient condition for the formation of apparent
horizon covering the singularity has been derived. For a polytrope having the
EoS $p=K\rho^{1+\frac{1}{n}}$, the scale factor ($A$) as a function of fluid
density ($\rho$) has been obtained which is then used to study the dynamics of
the fluid. Role of the polytropic index ($n$) and the constant of
proportionality ($K$) in the dynamics of the fluid is also studied. A new type
of exotic matter field having varied dependence of scale factor on the density,
and having the potential to give rise to bouncing cosmology, provided it is the
dominating fluid in the universe, is obtained in this domain and is
investigated. Energy conditions are discussed.
