In this article, molecular dynamics based simulations were carried out to study the tensile behaviour of boron nitride nanosheets (BNNSs). Four different sets of Tersoff potential parameters were used in the simulations for estimating the interatomic interactions between boron and nitrogen atoms. Modifications were incorporated in the Tersoff cut-off function to improve the accuracy of results with respect to fracture stress, fracture strain and Young's modulus. In this study, the original cut-off function was optimised in such a way that small and large cut-off distances were made equal, and hence a single cut-off distance was used with all sets of Tersoff potential parameters. The single value of cut-off distance for the Tersoff potential was chosen after analysing the potential energy and bond forces experienced by boron and nitrogen atoms subjected to bond stretching. The simulations performed with the optimised cut-off function help in identifying the Tersoff potential parameters that reproduce the experimentally evaluated mechanical behaviour of BNNSs.