Question

A particle moves in x-y plane according to the equation $\overrightarrow{r}$ = ($\hat{i}+2\hat{j}$) A cos $\omega$. The motion of the particle is:

• A. on a straight line
• B. on an ellipse
• C. periodic
• D. simple harmonic

Answer 1

Answer: (A), (C), (D)

simple harmonic
periodic
on a straight line

$\overrightarrow{r}=(i+2i)A\cos et$

$x=r_x=A\cos wt\hat{i}$

$y=r_y=2A\cos wt\hat{i}$

So, $\frac{x}{1}=\frac{y}{2}$

$x=2y$

So, motion is straight line

$v_x=\frac{drx}{dt}=-A\left(\sin \right(wt\left)\right)w$

$s_x=\frac{d^{2}rx}{d{t}^2}=-A{w}^2\cos wt$

$a_x=-w^{2}rx$

Similarly $s_y=-2w^{2}ry$

$acceleration\alpha -s{w}^2$

So, $SHM$ and periodic

Option $a,c,d$