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6.System of Particles and Rotational Motion
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The position of a particle is given by : $\overrightarrow {r\,} = (\hat i + 2\hat j - \hat k)$ and momentum $\overrightarrow P = (3\hat i + 4\hat j - 2\hat k)$. The angular momentum is perpendicular to
A
$X$ - axis
B
$Y$ - axis
C
$Z$ - axis
D
Line at equal angles to all the three axes
Solution
$\mathop L\limits^ \to = \mathop r\limits^ \to \times \mathop p\limits^ \to = $ $\left| {\,\begin{array}{*{20}{c}}{\hat i\,\,}&{\hat j\,\,}&{\,\,\hat k}\\{1\,\,}&{\,2\,\,}&{ – 1}\\{3\,\,}&{\,4\,\,}&{ – 2}\end{array}\,} \right|$ $ = 0\hat i – \hat j – 2\hat k = – \hat j – 2\hat k$ and the X- axis is given by $i + 0\hat j + 0\hat k$
Dot product of these two vectors is zero $i.e.$ angular momentum is perpendicular to $X$ – axis.
Standard 11
Physics
