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Q. An object is tied to a string and rotated in a vertical circle of radius r. Constant speed is maintained along the trajectory.

If $\frac{{\mathrm{T}}_{\max }}{{\mathrm{T}}_{\min }}=2,\mathrm{where},{\mathrm{T}}_{\max }$ = maximum tension and
T_min = minimum tension, then $\frac{v^2}{rg}$ is

Answer 1

Dear Student ,
Here in this case ,

$$\begin{gathered} \frac{m{v}^2}{r}=T_h+mg \\ where{T}_{h}isthehighestpoint. \\ \frac{m{v}^2}{r}=T_{\lambda }-mg \\ Where{T}_{\lambda }isthelowestpoint. \\ But,\frac{T_{max}}{T_{min}}=\frac{T_{\lambda }}{T_h}=2 \\ \Rightarrow T_{\lambda }=2T_h \\ {T}_h+mg=2T_h-mg \\ \Rightarrow T_h=2mg \\ Hence\frac{{\displaystyle m{v}^2}}{{\displaystyle r}}=T_h+mg=3mg \\ So,\frac{{\displaystyle v^2}}{{\displaystyle rg}}=3. \end{gathered}$$
Regards