An object's center of mass is ______. Select all that apply. the point about which the net torque is zero the point about which an unconstrained rotation occurs the geometric center of the object the mass-weighted center of the object the point about which the angular momentum is zero
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The point about which the net torque is zero: This is true. The center of mass is the point where the sum of all torques acting on the object is zero. Show more…
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Forces, acting on the mass $m$ are shown in the figure. As $\vec{N}=m \vec{g}$ the net torque of these two forces about any fixed point must be equal to zero. Tension $T$, acting on the mass $m$ is a central force, which is always directed towards the centre $O$. Hence the moment of force $T$ is also zero about the point $O$ and therefore the angular momentum of the particle $m$ is conserved about $O .$ Let, the angular velocity of the particle be $\omega$, when the separation between hole and particle $m$ is $r$, then from the conservation of momentum about the point $O$, : $m\left(\omega_{0} r_{0}\right) r_{0}=m(\omega r) r$ or Now, from the second law of motion for $T=F=m \omega^{2} r$ Hence the sought tension;
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