Question

If \(\vec{r}\) is a position vector of the body and \(\vec{p}\) is linear momentum, \(\vec{r}=2\hat{i}+3\hat{j}-3\hat{k}\) and \(\vec{p}=2\hat{i}+4\hat{j}-5\hat{k}\).
The angular momentum of the body is

• A. \(-3\hat{i}+4\hat{j}+2\hat{k}\)
• B. \(-3\hat{i}-4\hat{j}+2\hat{k}\)
• C. \(-2\hat{i}+3\hat{j}+2\hat{k}\)
• D. \(-\hat{i}-2\hat{j}+\hat{k}\)

Hint:

Angular momentum is the cross product of the position vector and the linear momentum.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Angular momentum is \(\vec{L}=\vec{r}\times\vec{p}\), which is evaluated as a determinant.

Step 2: Set up
\(\vec{r}=(2,3,-3)\), \(\vec{p}=(2,4,-5)\)

Step 3: Components
\(L_x=3(-5)-(-3)(4)=-15+12=-3\)
\(L_y=(-3)(2)-2(-5)=-6+10=4\)
\(L_z=2(4)-3(2)=2\)

Step 4: Result
\(\vec{L}=-3\hat{i}+4\hat{j}+2\hat{k}\), option (A).

Final Answer:
The angular momentum is \(-3\hat{i}+4\hat{j}+2\hat{k}\). \[ \boxed{\text{(A) }-3\hat{i}+4\hat{j}+2\hat{k}} \]