Q153 / 200 · Manipal (MET) 2012 · Physics
A particle is moving along a circular path of radius 5 m with a uniform speed $5 \mathrm{~ms}^{-1}$. What will be the average acceleration when the particle completes half revolution?
- AZero
- B$10 \mathrm{~ms}^{-2}$
- C$10 \pi \mathrm{~ms}^{-2}$
- Correct answerD$\frac{10}{\pi} \mathrm{~ms}^{-2}$
Solution
When the particle completes half revolution, change in velocity
$\Delta v=[5-(-5)] \mathrm{m} / \mathrm{s}=10 \mathrm{~m} / \mathrm{s}$
Time taken to complete the half revolution is $t=\frac{\pi r}{v}=\frac{\pi \times 5}{5}=\pi \mathrm{s}$
Thus, average acceleration $=\frac{\Delta v}{t}=\frac{10}{\pi} \mathrm{~m} / \mathrm{s}^2$
Time taken to complete the half revolution is $t=\frac{\pi r}{v}=\frac{\pi \times 5}{5}=\pi \mathrm{s}$
Thus, average acceleration $=\frac{\Delta v}{t}=\frac{10}{\pi} \mathrm{~m} / \mathrm{s}^2$
Hence, the correct answer is option: 'D'.