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A particle tied to one end of a string is being rotated in a vertical circle with constant frequency. The tension in the string at points $A, B, C$ and $D$ are $T_1, T_2, T_3$ and $T_4$ respectively Then
$T_1 = T_2 = T_3 = T_4$
$T_1 > T_2 > T_3,\,T_2 = T_4$
$T_1 > T_3 > T_2,\,T_2 = T_4$
$T_1 < T_2 < T_3,\,T_2 = T_4$
Solution
$\mathrm{T}_{\mathrm{A}}-\mathrm{mg}=\mathrm{m} \omega^{2} \mathrm{r}$
$\mathrm{T}_{1}=\mathrm{mg}+\mathrm{m} \omega^{2} \mathrm{r}$ $…(1)$
$\mathrm{T}_{\mathrm{B}}=\mathrm{T}_{2}=\mathrm{m} \omega^{2} \mathrm{r}$ $…(2)$
$\mathrm{T}_{\mathrm{C}}+\mathrm{mg}=\mathrm{m} \omega^{2} \mathrm{r}$
$\mathrm{T}_{3}=\mathrm{m} \omega^{2} \mathrm{r}-\mathrm{mg}$ $…(3)$
$\mathrm{T}_{\mathrm{D}}=\mathrm{T}_{4}=\mathrm{m} \omega^{2} \mathrm{r}$ $…(4)$
$\mathrm{T}_{1}>\mathrm{T}_{2}>\mathrm{T}_{3}$ and $\mathrm{T}_{2}=\mathrm{T}_{4}$
