First slide

Torque

Question

A force of $F = 2 i + 3 j - 2 k$ acts at a point (2, –3, 1). Then magnitude of torque about point (0,0,2) will be

Moderate

A

6 units
B

$3 \sqrt{5} u n i t s$
C

$6 \sqrt{5} u n i t s$
D

8 units

Solution

$\begin{array}{l} H e r e \vec{r} = (2 - 0) i + j (- 3 - 0) + k (1 - 2) \\ = 2 i - 3 j - k \end{array}$
$\begin{array}{l} \bar{τ} = \bar{r} \times \bar{F} = \begin{matrix} i & j & k \\ 2 & - 3 & - 1 \\ 2 & 3 & - 1 \end{matrix} \\ = 6 i + 12 k = 6 \sqrt{5} \end{array}$

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