A uniform sphere of mass \( m \), radius \( r \) and moment of inertia \( I \) about its centre ...

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A uniform sphere of mass \( m \), radius \( r \) and moment of inertia \( I \) about its centre moves along the \( x \)-axis as shown in
\( \mathrm{W} \) figure. Its centre of mass moves with velocity \( =v_{0} \), and it rotates about its centre of mass with angular velocity \( =\omega_{0} \). Let \( \vec{L}=\left(I \omega_{0}+m v_{0} r\right)(-\hat{k}) \). The angular momentum of the body about the origin \( O \) is
(1) \( \vec{L} \), only if \( v_{0}=\omega_{0} r \)
(2) greater than \( \vec{L} \), if \( v_{0}\omega_{0} r \)
(3) less than \( \vec{L} \), if \( v_{0}\omega_{0} r \)
(4) \( \vec{L} \), for all values of \( \omega_{0} \) and \( v_{0} \)
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