# 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 $\u2206T=1kgwt.=gN$. Therefore,

$\left(\frac{m{v}^{2}}{l}+mg\right)-\left(\frac{m{v}^{2}}{l}-mg\right)=g\Rightarrow 2mg=g\Rightarrow 2m=1\phantom{\rule{0ex}{0ex}}\Rightarrow m=0.5kg$

Hope this information will clear your doubts about the topic.

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