MCQ
The component of a vector $r$ along $X-$axis will have maximum value if
- A$r$ is along positive $Y-$axis.
- ✓$r$ is along positive $X-$axis.
- C$r$ makes an angle of $45^\circ $ with the $X-$axis.
- D$r$ is along negative $Y-$axis.
✓
Answer
Correct option: B.
$r$ is along positive $X-$axis.
Consider a vector $\vec{\text{R}}$ in $X-Y$ plane as shown in figure. If we draw orthogonal vectors $\vec{\text{R}}_{\text{x}}$ and $\vec{\text{R}}_{\text{y}}$ along $x$ and $y$ axes respectively, by law of vector addition, $\vec{\text{R}}=\vec{\text{R}}_{\text{x}}+\vec{\text{R}}_{\text{y}}$
The magnitude of component of $r$ along $X-$axis
$\text{r}_\text{x}=|\text{r}|\cos\theta$
$(\text{r}_\text{x})_{\text{maximum}}=|\text{r}|(\cos\theta)_{\text{maximum}}$
$\text{r}_\text{x}=|\text{r}|\cos\theta$
$=|\text{r}|\cos0^\circ=|\text{r}|$ $(\because\cos\theta$ is maximum if $\theta=0^\circ)$
As $\theta=0^\circ,$
$r$ is along positive $x-$axis.
The magnitude of component of $r$ along $X-$axis
$\text{r}_\text{x}=|\text{r}|\cos\theta$
$(\text{r}_\text{x})_{\text{maximum}}=|\text{r}|(\cos\theta)_{\text{maximum}}$
$\text{r}_\text{x}=|\text{r}|\cos\theta$
$=|\text{r}|\cos0^\circ=|\text{r}|$ $(\because\cos\theta$ is maximum if $\theta=0^\circ)$
As $\theta=0^\circ,$
$r$ is along positive $x-$axis.
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