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
$\frac{\text { Tangential acceleration }}{\text { Radial acceleration }}=\frac{\alpha r}{v^{2}} \times r=\frac{\alpha r^{2}}{v^{2}}$