A 200 MeV, 10 mA, medium energy high intensity proton accelerator (MEHIPA) is proposed to form the second stage of the Indian accelerator-driven system program. The linac consists of a normal conducting 3 MeV radio frequency quadrupole (RFQ) and a 200 MeV superconducting section consisting of three different families of single spoke resonators (SSR-A, SSR-B, and SSR-C). Here we discuss a detailed physics design of MEHIPA, including electro-magnetic design, multipacting analysis, higher-order mode studies, and beam dynamics.We have designed a compact linac, by careful optimization of cavity β for the superconducting section. We also performed detailed optimization studies on the linac lattice and transport line parameters, aimed at minimizing the emittance and beam halo. Reliability analysis and error studies were performed on this optimized linac, including various beam, cavity, and magnet parameters, to estimate the operation tolerances, and the results are reported for a maximum emittance growth of 50%.