Please explain the circled part of 5.21 please explain this experts

Dear Student,
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To perform a circular motion a body need centripetal force. The planets revolve around sun and centripetal force is provided by gravitation force. In this case force is provided by tension in the string.
So tension will be equal to centripetal force required to move stone in circular path.

$F_c=m{\omega }^{2}r=\frac{m{v}^2}{r}$
$$\begin{gathered} \left(i\right) \frac{40 rev}{min}=\frac{40 rev}{60 sec}=\frac{40\times 2\pi }{60 sec} [1 revolution=2\pi ] \\ \omega =\frac{4\pi }{3} \\ T=F_c=m{\omega }^{2}r=0.25\times 1.5\times {\left(\frac{4\pi }{3}\right)}^2=6.6N \\ \left(ii\right) \\ If tension is maximum, speed will be maximum. \\ {T}_{max}=F_c=\frac{m{v}^2}{r} \\ v=\sqrt{\frac{200\times 1.5}{0.25}}=34.6m/s \end{gathered}$$

Regards,
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