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Question
A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin ____________.
Options
is zero
remains constant
goes on increasing
goes on decreasing
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Solution
remains constant
For angular momentum, we have
\[\overrightarrow{L} = m\left( \overrightarrow{r} \times \overrightarrow{v} \right)\]
\[ \overrightarrow{v} = v \hat i\text{ and }\overrightarrow{r} = x \hat i + y \hat j \]
So,\[\overrightarrow{L} = - mvy \hat k\]
m, v and y are constant; therefore, angular momentum remains constant.
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