  The next generation of ground-based interferometric gravitational wave
detectors will observe mergers of black holes and neutron stars throughout
cosmic time. A large number of the binary neutron star merger events will be
observed with extreme high fidelity, and will provide stringent constraints on
the equation of state of nuclear matter. In this paper, we investigate the
systematic improvement in the measurability of the equation of state with
increase in detector sensitivity by combining constraints obtained on the
radius of a $1.4 \, \mathrm{M}_{\odot}$ neutron star from a simulated source
population. Since the measurability of the equation of state depends on its
stiffness, we consider a range of realistic equations of state that span the
current observational constraints. We show that a single 40km Cosmic Explorer
detector can pin down the neutron star radius for a soft, medium and stiff
equation of state to an accuracy of 10m within a decade, whereas the current
generation of ground-based detectors like the Advanced LIGO-Virgo network would
take $\mathcal{O}(10^5)$ years to do so for a soft equation of state.
