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,

\(T = 8T_{0}\)

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