A particle executes S.H.M. according to equation x=10( cm ) [2 t+… - Vidyadip

MCQ

A particle executes $S.H.M.$ according to equation $x=10( cm ) \cos \left[2 \pi t+\frac{\pi}{2}\right]$, where $t$ is in second. The magnitude of the velocity of the particle at $t=\frac{1}{6} \,s$ will be .............. $cm / s$

A
$24.7$
B
$20.5$
C
$28.3$
✓
$31.4$

✓

Answer

Correct option: D.

$31.4$

d
(D)

$x=10 \cos \left[2 \pi t+\frac{\pi}{2}\right]$

At $t=\frac{1}{6} s$

$x=10 \cos \left[\frac{\pi}{2}+\frac{\pi}{3}\right]$

$x=-10 \sin \frac{\pi}{3}$

$x=-5 \sqrt{3}$

$v=\omega \sqrt{A^2-x^2}$

$v=2 \pi \sqrt{100-75}$

$v=10 \pi$

$v=31.4 \,cm / s$

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