Question

A particle is moving along a circular path of radius $5\text{m}$ with a uniform speed $5\text{m/s}$. What will be the average acceleration when the particle completes half revolution?

• A. Zero
• B. $10m{s}^{-2}$
• C. $10\pi m{s}^{-2}$
• D. $\frac{10}{\pi }m{s}^{-2}$

Answer 1

The correct option is D $\frac{10}{\pi }m{s}^{-2}$

After completing the half revolution, the direction of speed is reversed, so change in velocity when the particle completes half revolution is

$△v=5\text{m/s}-(-5\text{m/s})=10\text{m/s}$

Time taken to complete the half revolution is:
$t=\frac{\pi r}{v}=\frac{\pi \times 5}{5}=\pi$ seconds

Hence average acceleration $=\frac{△v}{t}=\frac{10}{\pi }{\text{m/s}}^2$

Hence, option D is the correct answer.