Question

A car is travelling with a linear velocity $v$ on a circular road of radius $r$. If it is increasing its speed at the rate of $a m / s ^{2}$, then the resultant acceleration will be

• A. $\sqrt{\frac{v^{2}}{r^{2}}-a^{2}}$
• B. $\sqrt{\frac{v^{4}}{r^{2}}+a^{2}}$
• C. $\sqrt{\frac{v^{4}}{r^{2}}-a^{2}}$
• D. $\sqrt{\frac{v^{2}}{r^{2}}+a^{2}}$

Answer 1

Answer: (B)

$\sqrt{\frac{v^{4}}{r^{2}}+a^{2}}$

Answer 2

Centripetal acceleration $=\frac{v^{2}}{r}$ and it is perpendicular to increase in speed a which is tangential $\therefore$ Resultant acceleration $=\sqrt{\left(\frac{v^{2}}{r}\right)^{2}+\left(a^{2}\right)}$