An object of mass $8 \; kg$ is whirled round in a vertical circle of radius $2 \; m$ with a constant speed of $6 \; m/s$. Calculate the maximum and the minimum tension in the string.

Given,

Mass of the object $(m) = 8\;kg$

Radius of the object $(r) = 2\;m$

Speed of the object $(v) = 6\;m/s$

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

Minimum tension $(T_{min}) = \;?$

We have,

$T_{max} = \frac{m\;v^2}{r} + m\;g = \frac{8 \; * \; 6^2}{2} + 8\;*\;10 = 224\;N$

∴ Maximum tension $(T_{max}) = \;224\;N$

$T_{min} = \frac{m\;v^2}{r} - m\;g = \frac{8 \; * \; 6^2}{2} - 8\;*\;10 = 64\;N$

∴ Minimum tension $(T_{min}) = \;64\;N$

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