If the attached cable $OC$ is drawn inward such that the radial coordinate $r$ changes with a constant speed of $r^{}=-0\mathrm{.}5\frac{m}{s},$

determine the tension it exerts on the sled at the instant $r=2m.$ The sled and girl have a total mass of $50$ kg $.$ Neglect the

size of the girl and sled and the effects of friction between the sled and ice. Hint: First show that the equation of motion in the $$

direction yields $a_{}=r{}^{}+2r^{}{}^{}=(\frac{1}{r})\frac{d}{d}t(r^2({}^{}))=0.$ When integrated, $r^2{}^{}=C,$ where the constant $C$ is determined

from the problem data.