Question

Magnitude of torque of $\overrightarrow{F}=2\hat{i}-\hat{j}-\hat{k}$ acting at $(-5,2,1)$ about the origin is :

• A. $\sqrt{11}$
• B. $11$
• C. $\sqrt{180}$
• D. $21$

Answer 1

The correct option is C $\sqrt{180}$

Magnitude of force

$F=\sqrt{{\left(2\right)}^2+{\left(-1\right)}^2+{\left(-1\right)}^2}$

$F=\sqrt{6}N$

Distance of the point $\left(-5,2,1\right)$ from origin is given by

$r=\sqrt{{\left(-5-0\right)}^2+{\left(2-0\right)}^2+{\left(1-0\right)}^2}$

$r=\sqrt{30}m$

Now torque is

$\tau =F\times r$

$\tau =\sqrt{30\times 6}$

$\tau =13.42Nm$