A stone with mass $0.8 \; kg$ is attached to one end of a string $0.9 \; m$ long. The string will break if its tension exceeds $600 \; N$. The stone is whirled in a horizontal circle, the other end of the string remains fixed. Find the maximum speed, the stone can attain without breaking the string.

Given,

Mass of stone $(m) = 0.8\;kg$

Length of string $(r) = 0.9\;m$

Maximum tension $(T_{max}) = 600\;N$

Maximum speed $(v_{max}) = \;?$

For maximum speed at which the string will not break,

$T_{max} = \frac{m\;v^2_{max}}{r}$

$v^2_{max} = \frac{T_{max}\;r}{m} = \frac{600\;*\;0.9}{0.8} = 675$

⇒ $v = 25.98\;m/s$

∴ The maximum speed $(v_{max}) = \;25.98\;/m/s$

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