A mass of 100, g is tied to one end of a stri | vedclass

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(D) The maximum tension $T_{max}$ in the string is provided by the centripetal force required for circular motion.$T_{max} = m \omega^2 r$Given:Mass $

Vedclass · Accepted Answer

$87.64$

Vedclass · Answer

(D) The maximum tension $T_{max}$ in the string is provided by the centripetal force required for circular motion.$T_{max} = m \omega^2 r$Given:Mass $m = 100\, g = 0.1\, kg$Radius $r = 2\, m$Frequency $n = 200\, 	ext{rev/min} = \frac{200}{60}\, 	ext{rev/s} = \frac{10}{3}\, 	ext{Hz}$Angular velocity $\omega = 2\pi n = 2\pi 	imes \frac{10}{3} = \frac{20\pi}{3}\, 	ext{rad/s}$Substituting these values into the formula:$T_{max} = 0.1 	imes \left(\frac{20\pi}{3}ight)^2 	imes 2$$T_{max} = 0.1 	imes \frac{400\pi^2}{9} 	imes 2$$T_{max} = \frac{80\pi^2}{9} \approx \frac{80 	imes 9.8696}{9} \approx 8.888 	imes 9.8696 \approx 87.73\, N$Using $\pi^2 \approx 9.86$,$T_{max} = \frac{80 	imes 9.86}{9} \approx 87.64\, N$.Thus,the correct option is $D$.

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