a stone tied to a string is whirled in a vertical circle with uniform speed. if the difference between the max and min tensions is 1kgwt, the mass of the stone is? (ans :0.5 k)

Dear Student,

Please find below the solution to the asked query:

If a stone is tied to a string and whirled in a vertical circle, then,

When the stone is at its lowest point, tension in the string will be maximum as,

$T_{max}=mg+\frac{m{v}^2}{l}$
Where, m is the mass of the stone, v is the speed of the stone and l is the length of the stone.

When the stone is at its highest point, the tension in the string will be minimum as,


$T_{min}=\frac{m{v}^2}{l}-mg$
Given that the difference of maximum and minimum tensions is equal to $∆T=1 kg wt. = g N$. Therefore,

$$\begin{gathered} \left(\frac{m{v}^2}{l}+mg\right) - \left(\frac{m{v}^2}{l}-mg\right)=g \Rightarrow 2mg=g \Rightarrow 2m=1 \\ \Rightarrow m=0.5 kg \end{gathered}$$

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