On a disc of radius R a concentric circle of radius R/2 is drawn. The disc is free to rotate about a frictionless axis through its centre and perpendicular to plane of the disc. All the three forces (in plane of the disc) shown in figure are act tangentially to their respective circular periphering. The magnitude of the net torque (about centre of disc) acting on the disc is:-

Question

G1 Physics · Accepted Answer

All forces are tangential. Add torques algebraically about the centre using τ=rF. The net magnitude is 1.5FR, hence D. Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 1.5FR..