Question

For a particle undergoing linear SHM about x=0 ,choose the correct possible combination.Symbols have their usual meaning

Answer 1

For (D)$v\times a=0$
Since, angle between acceleration and velocity vector is either 0 or 180 which gives
$\overrightarrow{v}\times \overrightarrow{a}=0$
Therefore, there is no option for (D) it is never true
For (A)It is true when $\overrightarrow{v}$ and $\overrightarrow{a}$ are in same direction and there magnitude is also non zero. Therefore, it is true everywhere else extreme and mean position therefore,

A->3,4
(B)Velocity $v>0$ as well as $v<0$ except at extreme positions where velocity $v=0$
B->2,3,4
(C) acceleration $a<0$ for $0<x\le A$ and at extreme position
therefore,
C->1,3