Let's apply the Newton's Second Law of Motion in projections on axis "x" and "y":
"Tsin\\theta=\\dfrac{mv^2}{r},""Tcos\\theta=mg."
We can find the tension in the string from the second equation:
"T=\\dfrac{mg}{cos\\theta}."We can find angle "\\theta" from the geometry:
"sin\\theta=\\dfrac{r}{L},""\\theta=sin^{-1}(\\dfrac{r}{L})=sin^{-1}(\\dfrac{0.8\\ m}{1\\ m})=53^{\\circ}."Finally, we can calculate the tension in the string:
"T=\\dfrac{1\\ kg\\cdot9.8\\ \\dfrac{m}{s^2}}{cos53^{\\circ}}=16.3\\ N."
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