System of Particles and Rotational Motion - Result Question 19
19. Find the torque about the origin when a force of $3 \hat{j} N$ acts on a particle whose position vector is $2 \hat{k} m$.
[2020]
(a) $6 \hat{j} Nm$
(b) $-6 \hat{i} Nm$
(c) $6 \hat{k} Nm$
(d) $6 \hat{i} Nm$
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Answer:
Correct Answer: 19. (b)
Solution:
- (b) Given:
Force, $\vec{F}=3 \hat{j} N$
Position vector, $\vec{r}=2 \hat{k} m$
Torque, $\vec{\tau}=\vec{r} \times \vec{F}=2 \hat{k} \times 3 \hat{j}=6(\hat{k} \times \hat{j})=6(-\hat{i})$
$\Rightarrow \vec{\tau}=-6 \hat{i} Nm$
