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 `vecL_O and vecL_P` respectively, then.

Options

A. `overset rarr(L_(0))` and `overset rarr(L_(P))` do not vary wit time
B. `overset rarr(L_(0))` varies wit time while `overset rarr(L_(P))` remains constant
C. `overset rarr(L_(0))` remains consatnt, while `overset rarr(L_(P))` varies with time
D. `overset rarr(L_(0)) and overset rarr(L_(P))` both vary with time

Answer

C

Explanation

In Fig. weight `mg` of the mass acts vertically downwards and tension `T` in the string acts along `KP`. Two rectangular componets of `T` are `T cos theta` opposite to mg and `T sin theta` along `KO`.

About `O`, torques due to `T cos theta` and `mg` cancel out. Torque due to `T sin theta` is zero. Therefore, net torque about `O` is zero.
As `tau_(0) = (dL_(0))/(dt)`, therefore, `overset rarr(L_(0)) = `constant
i.e. `overset rarr(L_(0))` does not very time.
About `P`, torque due to T is zero, but torque due to `mg != 0`.
As `tau_(P) (dL_(P))/(dt) != 0`
`:. overset rarr(L_(P))` is not constant. It varies with time.
Choice (c) is correct.