Q. The position of a particle is given by r=$\widehat{\text{i}}$ + 2$\widehat{\text{j}}$ - $\widehat{k}$ and its linear momentum is given by p = 3 $\widehat{\text{i}}$ + 4 $\widehat{\text{j}}$ - 2 +$\widehat{k}\ $then its angular momentum, about the origin is perpendicular to
A) $yz$-plane
B) $z$-axis
C) $y$-axis
D) $x$-axis
Explanation
(d) $\mathbf{L} = \mathbf{r} \times \mathbf{P} = \left| \begin{matrix}
\widehat{\mathbf{i}} & \widehat{\mathbf{j}} & \widehat{\mathbf{k}} \\
1 & 2 & - 1 \\
3 & 4 & - 2
\end{matrix} \right|\ $
$\mathbf{L} = \widehat{\mathbf{i}}( - 4 + 4) - \widehat{\mathbf{j}}( - 2 + 3) + \widehat{\mathbf{k}}(4 - 6) = - \widehat{\mathbf{j}} - 2\widehat{\mathbf{k}}$
$\mathbf{L}$ has components along $–y$ axis and $–z$ axis.
The angular momentum is in $y - z$ plane $ie$., perpendicular to $x$-axis.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.