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6.System of Particles and Rotational Motion
medium
The position vectors of radius are $2\hat i + \hat j + \hat k$ and $2\hat i - 3\hat j + \hat k$ while those of linear momentum are $2\hat i + 3\hat j - \hat k.$ Then the angular momentum is
A$2\hat i - 4\hat k$
B$4\hat i - 8\hat k$
C$2\hat i - 4\hat j + 2\hat k$
D$4\hat i - 8\hat j$
Solution
(b) Radius vector $\vec r = \overrightarrow {{r_2}} – \overrightarrow {{r_1}} = (2\hat i – 3\hat j + \hat k) – (2\hat i +\hat j + \hat k)$
$\vec r = – 4\hat j$
Linear momentum $\overrightarrow p = 2\hat i + 3\hat j – \hat k$
$\vec L = \vec r \times \vec p = ( – 4\hat j) \times (2\hat i + 3\hat j – \hat k)$
$ = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\0&{ – 4}&0\\2&3&{ – 1}\end{array}\,} \right|$
$ = 4\hat i – 8\hat k$
$\vec r = – 4\hat j$
Linear momentum $\overrightarrow p = 2\hat i + 3\hat j – \hat k$
$\vec L = \vec r \times \vec p = ( – 4\hat j) \times (2\hat i + 3\hat j – \hat k)$
$ = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\0&{ – 4}&0\\2&3&{ – 1}\end{array}\,} \right|$
$ = 4\hat i – 8\hat k$
Standard 11
Physics
