A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l$ . The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

$\frac{ml\omega^{2}}{k - m\omega^{2}}$

A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l$ . The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :}

$\frac{ml\omega^{2}}{k - m\omega^{2}}$

$\frac{ml\omega^{2}}{k - \omega m}$

$\frac{ml\omega^{2}}{k - m\omega^{2}}$

$\frac{ml\omega^{2}}{k + m\omega^{2}}$

$\frac{ml\omega^{2}}{k + m\omega}$

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The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.