  Our present study involves the strange stars model in the framework of
$f(R,T)$ theory of gravitation. We have taken a linear function of the Ricci
scalar $R$ and the trace $T$ of the stress-energy tensor $T_{\mu \nu}$ for the
expression of $f(R,T)$, i.e., $f(R,T)=R+ 2 \gamma T $ to obtain the proposed
model, where $\gamma$ is a coupling constant. Moreover, to solve the
hydrostatic equilibrium equations, we consider a linear equation of state
between the radial pressure $p_r$ and matter density $\rho$ as $p_r=\alpha
\rho-\beta$, where $\alpha$ and $\beta$ are some positive constants, Both
$\alpha,\,\beta$ depend on coupling constant $\gamma$ which have been also
depicted in this paper. By employing the Krori-Barua {\em ansatz} already
reported in the literature [J. Phys. A, Math. Gen. 8:508, 1975] we have found
the solutions of the field equations in $f (R, T )$ gravity. The effect of
coupling constant $\gamma$ have been studied on the model parameters like
density, pressures, anisotropic factor, compactness, surface redshift, etc.
both numerically and graphically. A suitable range for $\gamma$ is also
obtained. The physical acceptability and stability of the stellar system have
been tested by different physical tests, e.g., the causality condition, Herrera
cracking concept, relativistic adiabatic index, energy conditions, etc. One can
regain the solutions in Einstein gravity when $\gamma\rightarrow 0$
