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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion1 Mark
Question
In a rotating body, $\text{a}=\alpha\text{r}$ and $\text{v}=\omega\text{r}.$ Thus $\frac{\text{a}}{\alpha}=\frac{\text{v}}{\omega}.$ Can a co you use the theorems of ratio and proportion studied in algebra so as to write $\frac{\text{a}+\alpha}{\text{a}-\alpha}=\frac{\text{v}+\omega}{\text{v}-\omega}$
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Answer

No, we cannot use componendo-dividendo theorem of proportion here. This is because $\alpha$ and a, and v and $\omega$ are dimensionally different. Therefore, ​$\text{v}+\omega$ and/ or $\alpha+\text{a}$ are not possible.

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