A small mass \( m \) is attached to a massless string whose other end is fixed at \( P \) as sho...

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A small mass \( m \) is attached to a massless string whose other end is fixed at \( P \) as shown in the figure. The mass is undergoing circular motion in the \( x-y \) plane with centre at \( O \) and constant angular speed \( \omega \). If the angular momentum of the system, calculated about \( O \) and \( P \) are denoted by \( \vec{L}_{O} \) and \( \vec{L}_{P} \) respectively, then
(1) \( \vec{L}_{O} \) and \( \vec{L}_{P} \) do not vary with time.
(2) \( \vec{L}_{O} \) varies with time while \( \vec{L}_{P} \) remains constant.
(3) \( \vec{L}_{O} \) remains constant while \( \vec{L}_{P} \) varies with time.
(4) \( \vec{L}_{O} \) and \( \vec{L}_{P} \) both vary with time.
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