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  4. A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is ( K /π) rev . / min. The value of K is: (Assume the string is massless and unstretchable)

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Q. A boy ties a stone of mass $100\, g$ to the end of a $2\, m$ long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of $80\, N$. If the maximum speed with which the stone can revolve is $\frac{ K }{\pi} rev . / \min$. The value of $K$ is : (Assume the string is massless and unstretchable)

JEE MainJEE Main 2022Work, Energy and Power

Solution:

$T=M \, \omega^{2} R$
$T=80\, N $
$M=0.1 $
$ \omega=?$
$ R=2 \, m$
$80=0.1 \, \omega^{2}(2)$
$\omega^{2}=400$
$\omega=20$
$2 \pi f =20$
$f =\frac{10}{\pi} \frac{ rev }{ s }$
$=\frac{600}{\pi} \frac{ rev }{ \min }$