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(A) The centripetal force required for circular motion is provided by the tension in the string.$T = mr\omega^2$Given:Mass $m = 2 \ kg$Radius $r = 2 \

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$10$

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(A) The centripetal force required for circular motion is provided by the tension in the string.$T = mr\omega^2$Given:Mass $m = 2 \ kg$Radius $r = 2 \ m$Maximum tension $T_{\max} = 16000 \ N$Angular velocity $\omega = 2\pi f$,where $f$ is the frequency in rotations per second.Substituting the values into the formula:$T_{\max} = mr(2\pi f_{\max})^2$$16000 = 2 	imes 2 	imes 4\pi^2 f_{\max}^2$$16000 = 16\pi^2 f_{\max}^2$$f_{\max}^2 = \frac{16000}{16\pi^2} = \frac{1000}{\pi^2}$Using the approximation $\pi^2 \approx 10$:$f_{\max}^2 = \frac{1000}{10} = 100$$f_{\max} = \sqrt{100} = 10 \ 	ext{rotations per second}$.

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