Arod of length 1.2 m has non uniform linear mass density rho_li(x) in kilograms per meter given by rho_l(x) = a + bx^3, where x is the distance in meters from the left end of the rod. (a)what are the si units of a and b? (b) find the total mass of the rod if a = 2 and b = +5. (c)find the position of center of mass of the rod.

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.