Motion in a Plane - Result Question 16
18. Find the torque of a force $\vec{F}=-3 \hat{i}+\hat{j}+5 \hat{k}$ acting at the point $\vec{r}=7 \hat{i}+3 \hat{j}+\hat{k}$.
[1997]
(a) $-21 \hat{i}+3 \hat{j}+5 \hat{k}$
(b) $-14 \hat{i}+3 \hat{j}+16 \hat{k}$
(c) $4 \hat{i}+4 \hat{j}+6 \hat{k}$
(d) $14 \hat{i}-38 \hat{j}+16 \hat{k}$
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Answer:
Correct Answer: 18. (d)
Solution:
- (d) $\vec{F}=-3 \hat{i}+\hat{j}+5 \hat{k} ; \vec{r}=7 \hat{i}+3 \hat{j}+\hat{k}$
Torque $(\vec{\tau})=\vec{r} \times \vec{F}$
$=(7 \hat{i}+3 \hat{j}+\hat{k}) \times(-3 \hat{i}+\hat{j}+5 \hat{k})$
$=7 \hat{k}+35(-\hat{j})-9(-\hat{k})+15 \hat{i}-3 \hat{j}+(-\hat{i})$
$=14 \hat{i}-38 \hat{j}+16 \hat{k}$
