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Question

A mass is kept on a horizontal frictionless surfaces. It is attached to a string and rotates about a fix centre at an angular velocity ω0. If the length of the string and angular velocity are doubled, find tension in the string which was initially T0.

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Solution

Initial Angular velocity =ωo
Initial Length =l
Initial Tension, T=mlω2o=To
where, m is mass of the particle. If length and angular velocity are doubled:
l=2l
ω=2ωo
New Tension, T=mlω2
T=2ml×4ω2o
T=8mlωo
T=8To

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