Q. A car is travelling with 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) $\sqrt{\left\{ \frac{v^{2}}{r^{2}} - a^{2} \right\}}$
B) $\sqrt{\left\{ \frac{v^{4}}{r^{2}} + a^{2} \right\}}$
C) $\sqrt{\left\{ \frac{v^{4}}{r^{2}} - a^{2} \right\}}$
D) $\sqrt{\left\{ \frac{v^{2}}{r^{2}} + a^{2} \right\}}$
Explanation
(b) $a_{resultant} = \sqrt{a_{radial}^{2} + a_{tangential}^{2}} = \sqrt{\frac{v^{4}}{r^{2}} + a^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.