Question

A force $\overrightarrow{F}=2\hat{i}-3\hat{k}$ act on a particle at $\overrightarrow{r}=0.5\hat{j}-2\hat{k}$. The torque $\overrightarrow{\tau }$ acting on the particle relative to a point with co-ordinates (2.0 m, 0 m , -3.0 m) is :

• A. $(-3.0\hat{i}-4.5\hat{j}-\hat{k})N-m$
• B. $(3\hat{i}+6\hat{j}-\hat{k})N-m$
• C. $(-20\hat{i}+4.0\hat{j}+\hat{k})N-m$
• D. $(-1.5\hat{i}-4.0\hat{j}-\hat{k})N-m$

Answer 1

The correct option is D $(-1.5\hat{i}-4.0\hat{j}-\hat{k})N-m$

For $\overrightarrow{F}=2\hat{i}-3\hat{k}\overrightarrow{r}=0.5\hat{j}-2\hat{k}$

Torque acting relation to print $(2\hat{i},0\hat{j},-3\hat{k})$

${\overrightarrow{r}}_{rel}=2\hat{i}-0.5\hat{j}-1\hat{k}$

$T=\overline{r}\times F$

$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 0& -3\\ 2& -0.5& 1\end{array}\right|$

$=(-1.5\hat{i}-4\hat{j}-\hat{k})N-m$