Sol. $\mathrm{U}=\mathrm{Fr}$ [Using $U=$ Potential energy and $v=$ velocity, to avoid confusion between their symbols] ⇒ Force $=\frac{-\mathrm{dU}}{\mathrm{dr}}=-\mathrm{F}$ ⇒ Magnitude of force $=$ Constant $=$ F $$ \Rightarrow F=\frac{m v^2}{R} $$ $$ \Rightarrow \mathrm{mvR}=\frac{\mathrm{nh}}{2 \pi} $$ $$ \begin{aligned} & \Rightarrow \mathrm{F}=\frac{\mathrm{m}}{\mathrm{R}} \times \frac{\mathrm{n}^2 \mathrm{~h}^2}{4 \pi^2} \times \frac{1}{\mathrm{~m}^2 \mathrm{R}^2} \\ & \Rightarrow \mathrm{R}=\left(\frac{\mathrm{n}^2 \mathrm{~h}^2}{4 \pi^2 \mathrm{mF}}\right)^{1 / 3} \\ & \Rightarrow \mathrm{v}=\frac{\mathrm{nh}}{2 \pi \mathrm{mR}} \end{aligned} $$