## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$T_3 > T_1=T_4 > T_2$
The tension in the string provides the centripetal force to keep the objects moving in a circle. In general, the centripetal force is: $F = M~\frac{v^2}{R}$. We can write an expression for the tension in each case. $T_1 = m~\frac{v^2}{r}$ $T_2 = m~\frac{v^2}{2r}$ $T_3 = 2m~\frac{v^2}{r}$ $T_4 = 2m~\frac{v^2}{2r} = m~\frac{v^2}{r}$ We can write the tensions in order from largest to smallest: $T_3 > T_1=T_4 > T_2$