A stone of mass 1 kg tied to a light inextensible string of length \(l = \frac{10}{3} m\) is whirling in a circular path of radius l in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be \(10\,m/s^{2}\) , the speed of the stone at the highest point of the circle is
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Since the maximum tension T_i : in the string moving in the vertical circle is at the bottom and minimum
tension \Gamma_{i} is at the top.
\ \ \(T_a = \frac{mv^2}{l} - mg\) and \(\Gamma_{r} = \frac{mv^{2}}{l} - mg\)
\ \ \(\frac{T_b}{T_T} = \frac{\frac{mv^2}{l} + mg}{\frac{mv^2}{l} - mg} = \frac{4}{1}\) or \(\frac{v_{g}^{2} + gL}{v_{i}^{2} \cdot gL} = \frac{4}{1}\)
or v_{s}^{2} + gL = 4v_{i}^{2} - 4gL but v_s^2 = v_f^2 + 4 g l
\ \ v_i^2 + 4gL - gL = 4v_i^2 - 4gL ⇒ ⇒ 3v_f^2 = 9gl
\ \ \(v_i = -3 / g \times L = -3 \times 10 \times \frac{10}{3}\) or \(v_{\tau} \quad 10\,\mathrm{m/s}\)
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