Problem $2$: $(20$ points$)$ Each ball has a negligible size and a mass of $10$ kg and is attached to the end of a rod whose mass may be neglected. If the velocity of each ball is given by $v=(\frac{t^3}{12}+\frac{t}{2}+5)\frac{m}{s},$ where $t$ is seconds, determine the torque applied to the rod when $t=5s.$