Velocity & Acceleration in SHM question from NEET 2009 (AIPMT)

Answer: (c)

1. $v = \omega\sqrt{a^2 - x^2}$ with $\omega = \frac{2\pi}{T}$
2. $\sqrt{a^2 - \frac{a^2}{4}} = \frac{\sqrt{3}a}{2}$
3. $v = \frac{2\pi}{T}\cdot\frac{\sqrt{3}a}{2} = \frac{\pi a\sqrt{3}}{T}$
4. So the answer is (c) $\frac{\pi a\sqrt{3}}{T}$.