Which of the following quantities is always n | vedclass

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Question

(B) In $SHM$,the acceleration $\vec a$ is given by $\vec a = -\omega^2 \vec r$,where $\vec r$ is the displacement vector from the equilibrium position

Vedclass · Accepted Answer

$\vec a \cdot \vec r$

Vedclass · Answer

(B) In $SHM$,the acceleration $\vec a$ is given by $\vec a = -\omega^2 \vec r$,where $\vec r$ is the displacement vector from the equilibrium position.Taking the dot product of $\vec a$ and $\vec r$:$\vec a \cdot \vec r = (-\omega^2 \vec r) \cdot \vec r = -\omega^2 |\vec r|^2$.Since $\omega^2$ is always positive and $|\vec r|^2$ is always non-negative,the product $\vec a \cdot \vec r$ is always negative (except at the equilibrium position where it is zero).Therefore,the correct option is $B$.

Which of the following quantities is always negative in a $SHM$?

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