# A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates fixed center at an angular velocity ω0 . If the length of the string and angular velocity both are doubled, the tension in the string which was initially T0 is now ​

$$T_{0}=m\omega _{0}^{2}L$$

If the length of the string and angular velocity is doubled, then

$$T = m(2\omega _{0})^{2}\left ( 2L \right )$$

On further calculation, we get,

$$T = m4\omega _{0}^{2}2L\\T = 8m\omega _{0}^{2}L$$

We get,

$$T = 8T_{0}$$