Question

In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v=$ speed of the particle, $\alpha =$ angular acceleration)

• A. $\frac{{\alpha }^2{r}^2}{v}$
• B. $\frac{{\alpha }^{2}r}{v^2}$
• C. $\frac{\alpha r^2}{v^2}$
• D. $\frac{v^2}{\alpha r^2}$

Answer 1

Answer: (C)

Given, radius of circle $=r$
Speed of particle $=v$
Angular acceleration $=\alpha$
We know that,
tangential acceleration $=\alpha r...(i)$
Radial acceleration $=\frac{v^2}{r}...(ii)$
On dividing Eq. (i) by Eq. (ii), we get
$\frac{\text{ Tangential acceleration }}{\text{ Radial acceleration }}=\frac{\alpha r}{v^2}\times r=\frac{\alpha r^2}{v^2}$