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A small mass m is attached to a massless...

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.

A

`vecL_O and vecL_P` do not vary with time.

B

`vecL_O` varies with time while `vecL_P` remains constant

C

`vecL_O` remains constant while `vecL_P` varies with time

D

`vecL_O and vecL_P` both vary with time

Text Solution

Verified by Experts

The correct Answer is:
c
In figure, weight mg of the mass acts vertically downwards and tension T in the string acts along KP. Two rectangular components of T are `Tcostheta` opposite to mg and `Tsintheta` along KO.
About O, torque due to `Tcostheta` and mg cancel out. Torque due to `Tsintheta` is zero. Therefore, net torque about O is zero. As `vectauo = (dvecLo)/(dt)=0`, `therefore vecL_(O)`= constant
i.e., `vecL_(O)` does not vary with time.
About P, torque due to T is zero, but torque due to mg `ne` 0
As `vectau_(p)= (dvecL_(P))/(dt)ne 0`
`therefore vecL_(P)` is not constant. It varies with time.
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