Kinematics Question 301
Question: What is the value of linear velocity, if $ \vec{\omega }=3\hat{i}-4\hat{j}+\hat{k} $ and $ \vec{r}=5\hat{i}-6\hat{j}+6\hat{k} $ [CBSE PMT 1999; CPMT 1999, 2001; Pb. PMT 2000; Pb. CET 2000]
Options:
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{k} $
Correct Answer: 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}) $ $ = \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 0 & -4 & 0 \\ 2 & 3 & -1 \\ \end{vmatrix} $ $ =4\hat{i}-8\hat{k} $
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