If the angular momentum of a body is conserved about a point, Then is it true that the Linear momentum is also conserved?

Other problems: Check your Calibre

Cannot Be Determined.
False
True

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It cannot be determined because We know Angular momentum is conserved means L= constant or $\dfrac{dL}{dt} = 0$

So now , $\tau_{ext} = 0$

So no External torque is acting on it.

So it doesnt mean that No $F_{ext}$ is acting on it, As $\tau_{ext} = F_{ext} .r$

So If r=0 then also $\tau_{ext} = 0$

And If $F_{ext} = 0$ then also $\tau_{ext} = 0$

And Linear momentum is conserved when $F_{ext} = 0$

So it may or may not be,

So we cannot determine it by this statement.

Hence answer is $\boxed{\text{Cannot be determined}}$