Two particles A and B are moving in a circle of radius $R$ with constant speeds $v_1$ and $v_2$ respectively. They start from the same point at $t=0$. If they move in opposite directions, the time after which they meet is:

Solution

1. The total distance to be covered by both particles combined to meet is the circumference $2\pi R$.
2. Since they move in opposite directions, their relative speed is $v_1+v_2$.
3. The time taken to meet is $t=\frac{\text{Total Distance}}{\text{Relative Speed}}$.
4. Thus, $t=\frac{2\pi R}{v_1+v_2}$.
5. Hence the answer is (A).