Question

A car is moving in a circular path of radius $500m$ with a speed of $30m/s$. If the speed is increasing, at the rate of $2m/s^2$ the resultant acceleration will be

• A. $2m/s^2$
• B. $2.5m/s^2$
• C. $2.7m/s^2$
• D. $4m/s^2$

Answer 1

Answer: (C)

A body moving in circular motion, has radial $\left(a_R\right)$ and tangential acceleration $\left(a_T\right)$. Hence, resultant acceleration is given by

$a=\sqrt{a_T^2+a_R^2}$
Given, $a_T=2m/s^2$,
$a_R=\frac{v^2}{r}=\frac{30\times 30}{500}=1.8m/s^2$
$\therefore a=\sqrt{(1.8{)}^2+(2{)}^2}=\sqrt{7.24}$
$\Rightarrow a=2.69\approx 2.7m/s^2$