Given,

[latex] \frac{T_{1}}{T_{2}} = 4 [/latex] [latex] T_{1} = 4T_{2} [/latex]

Here

[latex] T_{1} [/latex] is maximium tension

[latex] T_{2} [/latex] is minimum tension

The difference between the maximum tension and minimum tension for a body in the vertical circle is

[latex] \Rightarrow T_{1} = 4T_{2} = 6 mg [/latex] [latex] \Rightarrow 4T_{2} – T_{1} = 6 mg [/latex] [latex] \Rightarrow 3T_{2} = 6 mg [/latex] [latex] \Rightarrow T_{2} = 2 mg [/latex]

Now,

The highest point minimum tension can be

[latex] T_{2} = \frac{mv^{2}}{r} – mg [/latex] [latex] 2 mg = \frac{mv^{2}}{r} – mg [/latex] [latex] 3mg = \frac{mv^{2}}{r} [/latex]

Therefore, [latex] v = \sqrt{3mgr} [/latex]

Here r = [latex] L = \frac{10}{3r} [/latex] [latex] v = \sqrt{3 * 10 * \frac{10}{3}} [/latex] [latex] v = \sqrt{100}m/s [/latex]

Therefore, [latex] 10 ms^{-1} [/latex]

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