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 $\omega$ . If the angular momentum of the system, calculated about O and P are denoted by $\overrightarrow{L_O}$ and $\overrightarrow{L_P}$ respectively, then

• A. the direction of $\overrightarrow{L_O}$ and that of $\overrightarrow{L_P}$ both vary with time.
• B. the direction of $\overrightarrow{L_O}$ remains constant while that of $\overrightarrow{L_P}$ varies with time
• C. the direction of $\overrightarrow{L_O}$ varies with time while that of $\overrightarrow{L_P}$ remains constant
• D. the direction of $\overrightarrow{L_O}$ and $\overrightarrow{L_P}$ do not vary with time

Answer 1

The correct option is B

the direction of $\overrightarrow{L_O}$ remains constant while that of $\overrightarrow{L_P}$ varies with time

$\overrightarrow{L_0}=m(\overrightarrow{v}\times \overrightarrow{OA})$

$\overrightarrow{L_0}$ direction is always along +ve z-direction.

$\overrightarrow{L_P}=m(\overrightarrow{v}\times \overrightarrow{PA})$

The direction of of $\overrightarrow{L_P}$ continuously changes