A certain string breaks when a weight of $25\;N$ acts on it. A mass of $500\;gm$ is attached to one end of the string of $1\;m$ long and is rotated in a horizontal in a horizontal circle. Find the greatest number of revolutions per minute which can be made without breaking the string?

Given,

 

Maximum string $(T_{max}) = 25 \; N$

Mass of the object $(m) = 500 \; gm = 0.5 \; kg$

Radius of circle $(r) = 1\;m$

Frequency $(f) = \; ?$

We have,

$T_{max} = $$\frac{mv^2}{r}$$ = m\;\omega^2\;r$ = Centripetal Force

or, $T_{max} = m\;(2\;\pi\;f)^2\;r$

$25 = 0.5 * 4\pi^2 * f^2 * 1$

$f^2 = $$\frac{25}{0.5\; * \;4\; *\; \pi^2 \;*\; 1}$$ = 1.266$ rev/sec

$f = 1.125\;$ rev/sec

⇒ $f = 1.125 * 60\;rpm = 67.5\;rpm$

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