A horizontal single$-$cylinder engine has a cylinder diameter of $100$ mm$,$ a stroke of $120$ mmand a connecting rod length of $250$ mm$.$ The mass of the piston is $07$ kg and that of the connecting rodis $2$ kg$.$ The centre of mass of the connecting rod is $100$ mm from the big end bearing centre and theeffect of the connecting rod mass may be allowed for by apportioning it between the two ends. Whenthe crank is $20\backslash$deg from the top dead centre position on the working stroke, the gas pressure is $700$ kN$/$m$2.($a$)$ Determine, for this position, the crankshaft torque when the speed is $2000$ r$/$min$.($b$)$ At what speed would the crankshaft torque be zero for this crank position, $($the gas pressureremaining unchanged$)?$