A stone of mass 1 kg tied to a light inextensible string of length 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/s2 , the speed of the stone at the highest point of the circle is
Since the maximum tension TB in the string moving in the vertical circle is at the bottom and minimum tension TT is at the top.
TB = mvB2L = mg and TT = mvT2L - mg
∴ TBTT = mvB2L+mgmvT2L−mg or vB2+gLvT2+gL = 41
or vB2 + gL = 4vT2 - 4gL but vB2 = vT2 + 4gL
∴ vT2 + 4gL +gL ⇒ 3 vT2 = 3gL
∴ vT2 = 3 × g × L = 3 × 10 × 103 or vT = 10 m/sec