Question

A particle is moving in a circle of radius $10$ cm with uniform speed, completing the circle in $4$ s. Find the magnitude of its acceleration.

• A. $\pi cm/s^2$
• B. $2.5{\pi }^{2}cm/s^2$
• C. ${\pi }^{2}cm/s^2$
• D. $2\pi cm/s^2$

Answer 1

The correct option is B $2.5{\pi }^{2}cm/s^2$

Answer is B.
The distance covered in completing the circle $2\pi r=2\pi \times 10cm$.
The linear speed is $v=2\pi r/t=\frac{2\pi \times 10cm}{4s}=5\pi cm/s$
The acceleration is $a=\frac{v^2}{r}=\frac{(5\pi cm/s{)}^2}{10cm}=2.5{\pi }^{2}cm/s^2$.
Hence, the magnitude of its acceleration is $=2.5{\pi }^{2}cm/s^2$.