Assertion : In simple harmonic motion, the velocity is maximum wh… - Vidyadip

MCQ

$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
✓
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

✓

Answer

Correct option: B.

If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.

b
At the middle point velocity of the particle under $SHM$ is maximum but acceleration is zero since displacement is zero. So Assertion is true.

We know that $x=a \sin \omega t$ $...(1)$

Where $x$ is displacement and a is amplitude.

Velocity $=\frac{d x}{d t}=a \omega \cos \omega t$

$=a \omega \cos (-\omega t)=a \omega \sin \left(\frac{\pi}{2}-(-\omega t)\right)$

$=a \omega \sin \left(\omega t+\frac{\pi}{2}\right)$ $...(2)$

From equation $( 1 )$ and $(ii)$ it is clear that

Velocity is ahead of displacement $(x)$ by $\frac{\pi}{2}$ angle.

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