Question

A particle is moving along a straight line.Find the magnitude of angular momentum about origin when particle is at minimum distance from origin.

• A. $12{\text{kg m}}^2\text{/s}$
• B. $6{\text{kg m}}^2\text{/s}$
• C. $8{\text{kg m}}^2\text{/s}$
• D. $10{\text{kg m}}^2\text{/s}$

Answer 1

The correct option is B $6{\text{kg m}}^2\text{/s}$

We know that, at minimum distance, line joining origin and particle is perpendicular to its path.
Given, equation of line,
$4y-3x=2$
$\Rightarrow y=\frac{3}{4}x+\frac{1}{2}$
On comparing with $y=mx+c$
$m=\frac{3}{4}$
$\Rightarrow \tan \theta =\frac{3}{4}\Rightarrow \theta ={37}^{\circ }$
$y$ intercept, $c=\frac{1}{2}\text{m}$

Minimum distance,
$r_{\perp }=\frac{1}{2}\times \sin {53}^o=\frac{2}{5}$
Now, angular momentum, $L$
$L=mv{r}_{\perp }$ $[\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}]$
$=3\times 5\times \frac{2}{5}$
$\Rightarrow L=6{\text{kg m}}^2\text{/s}$
The magnitude of angular momentum about origin at minimum distance from it is $6{\text{kg m}}^2\text{/s}$.