Torque

Practice Questions:

Question 11: easy

Find the torque of a force $\vec{F} = -3\hat{i} + \hat{j} + 5\hat{k}$ acting at the point $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$

(1997)

1. $-21\hat{i} + 4\hat{j} + 4\hat{k}$

2. $-14\hat{i} + 34\hat{j} - 16\hat{k}$

3. $14\hat{i} - 38\hat{j} + 16\hat{k}$

4. $4\hat{i} + 4\hat{j} + 6\hat{k}$

View Answer

Torque $\vec{\tau} = \vec{r} \times \vec{F}$.
Using the determinant method: $\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 7 & 3 & 1 \\ -3 & 1 & 5 \end{vmatrix}$.
$= \hat{i}(15 - 1) - \hat{j}(35 - (-3)) + \hat{k}(7 - (-9)) = 14\hat{i} - 38\hat{j} + 16\hat{k}$.

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Question 12: easy

What is torque of the force $\vec{F} = 2\hat{i} – 3\hat{j} + 4\hat{k}$ acting at the point $\vec{r} = 3\hat{i} + 2\hat{j} + 3\hat{k}$ about origin?

(1995)

1. $-6\hat{i} + 6\hat{j} - 12\hat{k}$

2. $-17\hat{i} + 6\hat{j} + 13\hat{k}$

3. $6\hat{i} - 6\hat{j} + 12\hat{k}$

4. $17\hat{i} - 6\hat{j} - 13\hat{k}$

View Answer

Torque is $\vec{\tau} = \vec{r} \times \vec{F}$.
$\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 3 \\ 2 & -3 & 4 \end{vmatrix}$.
$= \hat{i}(8 - (-9)) - \hat{j}(12 - 6) + \hat{k}(-9 - 4) = 17\hat{i} - 6\hat{j} - 13\hat{k}$.

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