Question

A car is travelling with linear velocity $v$ on a circular road of radius $r.$ If the speed is increasing at the rate of $am{s}^{-2}$ , 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. $\sqrt{\left[\frac{v^2}{r^2}+a^2\right]}$

Answer 1

Answer: (B)

We have given that the velocity of the car is increasing. Therefore, the motion of the car is a non-uniform circular motion. In the non-uniform circular motion, the total acceleration of the car is the sum of its tangential acceleration and radial acceleration (centripetal acceleration). That is, ${\overrightarrow{a}}_{net}={\overrightarrow{a}}_{cp}+{\overrightarrow{a}}_t$
$\Rightarrow a_{net}=\sqrt{a_{cp}^2+a_t^2}$ $=\sqrt{{\left(\frac{v^2}{r}\right)}^2+a^2}$ $=\sqrt{\frac{v^4}{r^2}+a^2}$ .