MHT CET · Physics · Rotational Motion
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 \(\overrightarrow{\mathrm{P}}\)
- 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
Answer & Solution
Correct Answer
(B) \(\overrightarrow{\mathrm{L}}\) is maximum when \(\overrightarrow{\mathrm{P}}\) is perpendicular to \(\overrightarrow{\mathrm{r}}\)
Step-by-step Solution
Detailed explanation
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 \(\theta=90^{\circ}\)
Its magnitude is \(\mathrm{L}=\mathrm{rp} \sin \theta\)
\(\mathrm{L}\) will be maximum when \(\theta=90^{\circ}\)
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