Question

A unit mass at position vector $\overrightarrow{r}=(3\hat{i}+4\hat{j})$ is moving with a velocity $\overrightarrow{v}=(5\hat{i}-6\hat{j})$ What is the angular momentum of the body about the origin

• A. 2 units along $z$ -axis
• B. 38 units along $x$ -axis
• C. 38 units along $y$ -axis
• D. 38 units along $Z$ -axis

Answer 1

The correct option is C 38 units along $y$ -axis

$\begin{array}{cc}\text{Given}-& \ast \text{Position vector}\overrightarrow{r}=3\hat{i}+4\hat{j}\\ & \ast \text{velocity vector}\overrightarrow{v}=5\hat{i}-6\hat{j}\end{array}$

$\begin{array}{c}\text{We know that angular momentum-}\\ \overrightarrow{L}=m\cdot (\overrightarrow{r}\times \overrightarrow{v})=\overrightarrow{r}\times \overrightarrow{v}(m=1\text{unit})\\ \overrightarrow{L}=(3\hat{i}+4\hat{j})\times (5\hat{i}-6\hat{j})\\ \overrightarrow{L}=-38\hat{k}\\ \text{Angular momentum is}38\text{units along}z\text{-axis}\\ \text{Hence, option (c) is correct.}\end{array}$