Question

A particle has the position vector $r=\hat{i}-2\hat{j}+\hat{k}$ and the linear momentum $p=2\hat{i}-\hat{j}+\hat{k}$. Its angular momentum about the origin is

• A. $-\hat{i}+\hat{j}-3\hat{k}$
• B. $-\hat{i}+\hat{j}+3\hat{k}$
• C. $\hat{i}-\hat{j}+3\hat{k}$
• D. $\hat{i}-\hat{j}-5\hat{k}$
• E. $\hat{i}-\hat{j}+5\hat{k}$

Answer 1

Answer: (B)

Given,
$r=\hat{i}-2\hat{j}+\hat{k}$
$p=2\hat{i}-\hat{j}+\hat{k}$
Angular momentum
$J=r\times p$
$=(\hat{i}-2\hat{j}+\hat{k})\times (2\hat{i}-\hat{j}+\hat{k})$
$J=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -2& 1\\ 2& -1& 1\end{array}\right|$
$J=\hat{i}(-2+1)-\hat{j}(1-2)+\hat{k}(-1+4)$
$J=-\hat{i}+\hat{j}+3\hat{k}$