Question

A car of mass $ m $ moves in a horizontal circular path of radius $ r $ meter. At an instant its speed is $ v\,m/s $ and is increasing at a rate a $ m/s^{2} $ , then the acceleration of the car is:

• A. $ \sqrt{a\left( \frac{{{v}^{2}}}{r} \right)} $
• B. $ \sqrt{{{a}^{2}}+{{\left( \frac{{{v}^{2}}}{r} \right)}^{2}}} $
• C. $ \frac{{{v}^{2}}}{r} $
• D. $ a $

Answer 1

The Correct Option is B

In the non-uniform circular motion, car will have radial and tangential acceleration.
In the non-uniform circular motion of the car, the car will have radial $\left(a_{R}\right)$ and tangential acceleration $\left(a_{T}\right)$ and both these accelerations will be perpendicular to each other.
Radial or centripetal acceleration, $a=\frac{v^{2}}{r}$

and tangential acceleration, $a_{T}=a$.
$\therefore$ Magnitude of resultant acceleration is
$a'=\sqrt{a_{R}^{2}+a_{T}^{2}}$
$a'=\sqrt{\left(\frac{v^{2}}{r}\right)^{2}+a^{2}}$