  In this article we try to present spherically symmetric isotropic strange
star model under the framework of $f(R,\mathcal{T})$ theory of gravity. To this
end, we consider that the Lagrangian density is an arbitrary linear function of
the Ricci scalar $R$ and the trace of the energy momentum tensor~$\mathcal{T}$
given as $f\left(R,\mathcal{T}\right)=R+2\chi T$. We also assume that the quark
matter distribution is governed by the simplest form of the MIT bag model
equation of state (EOS) as $p=\frac{1}{3}\left(\rho-4B\right)$, where $B$ is
the bag constant. We have obtained an exact solution of the modified form of
the the Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of
$f(R,\mathcal{T})$ gravity theory and studied the dependence of different
physical properties, viz., total mass, radius, energy density and pressure on
the chosen values of $\chi$. Further, to examine physical acceptability of the
proposed stellar model in detail, we conducted different tests, viz. energy
conditions, modified TOV equation, mass-radius relation, causality condition
etc. We have precisely explained the effects arising due to the coupling of the
matter and geometry on the compact stellar system. For a chosen value of the
Bag constant we have predicted numerical values of different physical
parameters in tabular format for the different strange stars. It is found that
as the factor $\chi$ increases the strange stars shrink gradually and become
less massive to turn into a more compact stellar system. The maximum mass point
is well within the observational limits and hence our proposed model is
suitable to explain the ultra dense compact stars. For $\chi=0$ we retrieve as
usual the standard results of general relativity (GR).
