A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \mathrm{~cm} / \mathrm{s}$. The wavelength of the wave is $0.5 \mathrm{~m}$ and its amplitude is $10 \mathrm{~cm}$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{~cm}$ is

• Correct answer
  A

  $\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$
• B

  $-\frac{\sqrt{3} \pi}{50} \hat{j} \mathrm{~m} / \mathrm{s}$
• C

  $\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$
• D

  $-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$

Hence, the correct answer is option: 'A'.