Q. A car is circulating on the path of radius $r$ and at any time its velocity is $v$ and rate of increases of velocity is $a$. The resultant acceleration of the car will be
A) $\sqrt{\frac{v^{2}}{a^{2}} + r^{2}}$
B) $\sqrt{\frac{v^{2}}{r} + a}$
C) $\sqrt{\frac{v^{4}}{r^{2}} + a^{2}}$
D) $\left( \frac{v^{2}}{r} + a \right)$
Explanation
(c) Resultant acceleration
$= \sqrt{\left( \begin{array}{r}
tangential \\
acceleration
\end{array} \right)^{2} + \left( \begin{array}{r}
centripetal \\
acceleration
\end{array} \right)^{2}}$
$= \sqrt{a^{2} + \left( \frac{v^{2}}{r} \right)^{2}} = \sqrt{\frac{v^{4}}{r^{2}} + a^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.