PYQ NEET- Rotational Motion L-6

Question: Find the torque about the origin when a force of $3 \hat{\mathbf{j}} \mathrm{N}$ acts on the particle whose position vector is $2 \hat{\mathbf{k}} \mathbf{m}$.#

A) $6 \hat{\mathbf{j}} \mathrm{N}-\mathrm{m}$

B) $-6 \hat{i} N-m$

C) $6 \hat{\mathbf{k}} \mathrm{N}-\mathrm{m}$

D) $6 \hat{\mathbf{i}} \mathrm{N}-\mathrm{m}$

Answer: $-6 \hat{i} N-m$#

Solution:#

Given, position vector, $\mathbf{r}=2 \hat{\mathbf{k}} \mathrm{m}$ Force, $\mathbf{F}=3 \hat{\mathbf{j}} \mathrm{N}$ As, torque, $$ \begin{aligned} \boldsymbol{\tau} & =\mathbf{r} \times \mathbf{F}=2 \hat{\mathbf{k}} \times 3 \hat{\mathbf{j}}=6(-\hat{\mathbf{i}}) \ & =-6 \hat{\mathbf{i}} \mathrm{N}-\mathrm{m} \end{aligned} $$

Hence, correct option is (b).