The disclosure, in one aspect, provides a method of drilling a wellbore that includes features of drilling the wellbore using a drilling assembly that includes a drill bit that further includes a weight sensor and a torque sensor, determining weight-on-bit using measurements from the weight sensor and torque-on-bit using measurement from the torque sensor during drilling of the wellbore, obtaining measurements for rotational speed of the drill bit and rate of penetration of the drill bit during drilling of the wellbore, determining mechanical specific energy of the bottomhole assembly using the determined weight-on-bit, torque-on-bit and obtained rotational speed of the drill bit and the obtained rate of penetration of the drill bit, and altering a drilling a parameter in response to the determined mechanical specific energy.