For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively and M = Mass on the sleeve)

A. $$\frac{{{\text{mg}} + {{\text{S}}_1}}}{{{\text{mg}} + {{\text{S}}_2}}} = \frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}}$$

B. $$\frac{{{\text{mg}} - {{\text{S}}_1}}}{{{\text{mg}} - {{\text{S}}_2}}} = \frac{{{{\text{r}}_2}}}{{{{\text{r}}_1}}}$$

C. $$\frac{{{{\text{S}}_1}}}{{{{\text{S}}_2}}} = \frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}}$$

D. $$\frac{{{{\text{S}}_2}}}{{{{\text{S}}_1}}} = \frac{{{{\text{r}}_1}}}{{{{\text{r}}_2}}}$$

Answer: Option A