An object of mass $0.5 \; kg$ is rotated in a horizontal circle by a string $1 \; m$ long. The maximum tension in the string before it breaks is $50 \; N$. What is the greatest number of revolutions per second of the object?

Given,

Mass of an object $(m) = 0.5\;kg$

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

Tension in the string $(T) = 50\;N$

Greatest number of revolution $(f) = \;?$

In case of horizontal circle, there is no maximum and minium tension. So we can write,

$T = m\; \omega^2\;r = m\;4\pi^2\;f^2\;r$

$f^2 = \frac{T}{4\;\pi^2\;m\;r}$

$f = \frac{1}{2\;\pi}\;\sqrt{\frac{T}{m\;r}} = \frac{1}{2\pi}\;\sqrt{\frac{50}{0.5\;*\;1}} = 1.6\;rev/sec$

⇒ Greatest number of revolution $(f) = \;1.6\;rev/sec$

Return to Main Menu