Question

The radius vector and linear momentum are respectively given by vectors $2 \hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+\hat{k}$. 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. $4 \hat{i}-8 \hat{j}$

Answer 1

Answer: (B)

Given radius vector, $\vec{r}=2 \hat{i}+\hat{j}+\hat{k}$ Linear momentum, $\vec{p}=2 \hat{i}-3 \hat{j}+\hat{k}$
As angular momentum, $\vec{L}=\vec{r} \times \vec{p}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 1 \\ 2 & -3 & 1\end{array}\right|$
$=\hat{i}(1-(-3))-\hat{j}(2-2)+\hat{k}(-6-2)=4 \hat{i}-8 \hat{k}$