A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length $ℓ$ . The system is rotated about the other end of the spring with an angular velocity $ω$ in gravity free space. The increase in length of the spring is

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The spring force supplies the centripetal force at radius ( ℓ + x ) : k x = m ω 2 ( ℓ + x ) . x ( k − m ω 2 ) = m ω 2 ℓ ⇒ x = k − m ω 2 m ω 2 ℓ ​ . Answer: (B)

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