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} $

Answer 1

The Correct Option is B

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