B

Step 1: Understand that the tension in the ring arises due to the centripetal acceleration required for circular motion.
Step 2: The formula for centripetal force is given by \( F_c = \frac{mv^2}{R} \).
Step 3: Since the entire ring is rotating, the required centripetal force is provided by the tension in the ring. Therefore, we can equate the tension (T) to the centripetal force:
\( T = \frac{mv^2}{R} \).
Step 4: Therefore, the tension in the ring is \( T = \frac{mv^2}{R} \) which leads to option B being correct, as it matches the provided equation.