Question

A force of $(2\widehat{i} - 4\widehat{j} + 2\widehat{k})$ N acts at a point $(3\widehat{i} + 2\widehat{j} - 4\widehat{k})$ metre from the origin. The magnitude of torque is

• A. Zero
• B. 24.4 N-m
• C. 0.244 N-m
• D. 2.444 N-m

Answer 1

Answer: (B)

24.4 N-m

Answer 2

$\overset{\rightarrow}{F} = (2\widehat{i} - 4\widehat{j} + 2\widehat{k})N$ and $\overset{\rightarrow}{r} = (3i + 2 - 4\widehat{k})$ meter

Torque $\overset{\rightarrow}{\tau} = \overset{\rightarrow}{r} \times \overset{\rightarrow}{F}$ $= \left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 3 & 2 & - 4 \\ 2 & - 4 & 2 \end{matrix} \right|$

⇒ $\overset{\rightarrow}{\tau} = - 12\widehat{i} - 14\widehat{j} - 16\widehat{k}$

and $|\overset{\rightarrow}{\tau}| = \sqrt{( - 12)^{2} + ( - 14)^{2} + ( - 16)^{2}}$= 24.4 N-m