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: (1) $\frac { m l \omega ^ { 2 } } { k - \omega m }$ (2) $\frac { m l \omega ^ { 2 } } { k - m \omega ^ { 2 } }$ (3) $\frac { m l \omega ^ { 2 } } { k + m \omega ^ { 2 } }$ (4) $\frac { m l \omega ^ { 2 } } { k + m \omega }$
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:\\
(1) $\frac { m l \omega ^ { 2 } } { k - \omega m }$\\
(2) $\frac { m l \omega ^ { 2 } } { k - m \omega ^ { 2 } }$\\
(3) $\frac { m l \omega ^ { 2 } } { k + m \omega ^ { 2 } }$\\
(4) $\frac { m l \omega ^ { 2 } } { k + m \omega }$