A small mass is attached to a massless string whose other end is fixed at as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed . If the angular momentum of the system, calculated abo

Question

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 $ω$ . If the angular momentum of the system, calculated about O and P are denoted by ${\vec{L}}_{O}$ and ${\vec{L}}_{P}$ respectively, then [2012]

Smart Achievers · Accepted Answer

(3)

For all locations of $m$ , the angular momentum of the mass $m$ about O i.e., $L_{O}$ is ${\vec{L}}_{P}$ 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.

Solution

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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Solution

1 L→O and L→P do not vary with time

2 L→O varies with time while L→P remains constant

3 L→O remains constant while L→P varies with time

4 L→O and L→P both vary with time

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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