The radius vector and linear momentum are respectively given by vector 2 hati+2 hatj+ hatk and 2 hati-2 hatj+ hatk . Their angular momentum is

Question

The radius vector and linear momentum are respectively given by vector 2 hati+2 hatj+ hatk and 2 hati-2 hatj+ hatk . Their angular momentum is (A) 2 hati-4 hatj (B) 4 hati-8 hatk (C) 2 hati-4 hatj+2 hatk (D) 4 hati-8 hatj

Tardigrade Admin · Accepted Answer

Angular momentum overset arrow textL = overset arrow textr × overset arrow textp =(2 hati + 2 hatj + hatk)× (2 hati - 2 hatj + hatk)=4 hati-8 hatk

Q. The radius vector and linear momentum are respectively given by vector $2 \hat{i} + 2 \hat{j} + \hat{k}$ and $2 \hat{i} - 2 \hat{j} + \hat{k}$ . Their angular momentum is

$2 \hat{i} - 4 \hat{j}$

$4 \hat{i} - 8 \hat{k}$

2 $\hat{i} - 4 \hat{j} + 2 \hat{k}$

4 $\hat{i} - 8 \hat{j}$

Angular momentum $L \to = r \to \times p \to$
$= (2 \hat{i} + 2 \hat{j} + \hat{k}) \times (2 \hat{i} - 2 \hat{j} + \hat{k}) = 4 \hat{i} - 8 \hat{k}$

Q. The radius vector and linear momentum are respectively given by vector 2i^+2j^​+k^ and 2i^−2j^​+k^ . Their angular momentum is

2i^−4j^​

4i^−8k^

2 i^−4j^​+2k^

4 i^−8j^​