JEE Advanced · Physics · 8. Rotational Motion
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
- A \(\vec{L}_{O}\) and \(\vec{L}_{P}\) do not vary with time
- B \(\vec{L}_{O}\) varies with time while \(\vec{L}_{P}\) remains constant
- C \(\vec{L}_{O}\) remains constant while \(\vec{L}_{P}\) varies with time
- D \(\vec{L}_{O}\) and \(\vec{L}_{P}\) both vary with time
Answer & Solution
Correct Answer
(C) \(\vec{L}_{O}\) remains constant while \(\vec{L}_{P}\) varies with time
Step-by-step Solution
Detailed explanation
For all locations of \(\mathrm{m}\) the angular momentum of the mass \(m\) about \(O\) i.e., \(L_{o}\) is \(m r^{2} \omega\) and is directed toward \(+z\) direction. The angular momentum of mass \(m\) about \(P\) i.e., \(L_{p}\) is \(m v l\) and is directed for the given location of \(m\) as shown in the figure. For different location of \(m\), the direction of \(\vec{L}_{P}\) remains changing.
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