  In this article, we studied the behavior of relativistic spherical objects
considering Tolman IV spacetime in modified $f(R,\,T)$ gravity for the
uncharged perfect fluid matter. We have chosen the matter Lagrangian as
$\mathcal{L}_m=-p$ to develop our present model. In particular, for this
investigation we have reported for the compact object LMC $X-4$ [Mass=$(1.04
\pm 0.09)M_{\odot}$; Radius= $8.301_{-0.2}^{+0.2}$ Km] in our paper. The effect
of the coupling parameter $\beta$ on the local matter distribution of compact
stars has been investigated in this paper. It can be seen that with greater
values of $\beta$, the sound speed and adiabatic index are higher. On contrary,
the mass function takes lower value for higher values of $\beta$. Our obtained
solution does not admit singularities in the matter density, pressure and
metric functions. According to our graphical analysis, this new stellar model
satisfies all physical requirements anticipated in a realistic star.
