Question

For a particle moving on a circular path of radius $5cm$, the velocity at an instant ‘$t$’ is $3\hat{i}+4\hat{j}m/s$. Assuming the particle to be in uniform circular motion, the value of centripetal acceleration is

• A. $180m/s^2$
• B. $320m/s^2$
• C. $980m/s^2$
• D. $500m/s^2$

Answer 1

The correct option is D $500m/s^2$

Centripetal acceleration $a_C=\frac{v^2}{r}=\frac{\overrightarrow{v}.\overrightarrow{v}}{r}$
$=\frac{(3\hat{i}+4\hat{j}).(3\hat{i}+4\hat{j})}{5\times {10}^{-2}}$
$=\frac{3^2+4^2}{5\times {10}^{-2}}=\frac{25}{5\times {10}^{-2}}=500m/s^2$