Q143 / 150 · MHT CET 2021 (22 Sep Shift 2) · Physics

A particle with position vector $\overrightarrow{\mathrm{r}}$ has a linear momentum $\overrightarrow{\mathrm{p}}$. Which one of the following statements is true in respect of its angular momentum ' $\overrightarrow{\mathrm{L}}$ ' about the origin?

  • A
    $\overrightarrow{\mathrm{L}}$ acts along $\overrightarrow{\mathrm{P}}$
  • Correct answer
    B
    $\overrightarrow{\mathrm{L}}$ is maximum when $\overrightarrow{\mathrm{P}}$ is perpendicular to $\overrightarrow{\mathrm{r}}$
  • C
    $\overrightarrow{\mathrm{L}}$ acts along $\overrightarrow{\mathrm{r}}$
  • D
    $\overrightarrow{\mathrm{L}}$ is maximum when $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{r}}$ are parallel

Solution

The angular momentum of the particle is given by $\overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}}$ Its magnitude is $\mathrm{L}=\mathrm{rp} \sin \theta$ $\mathrm{L}$ will be maximum when $\theta=90^{\circ}$

Hence, the correct answer is option: 'B'.

Relevant Questions