SATHEE: Kinematics Question 427

Kinematics Question 427

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

Options:

A) $14 \hat{i} - 38 \hat{j} + 16 \hat{k}$

B) $4 \hat{i} + 4 \hat{j} + 6 \hat{k}$

C) $21 \hat{i} + 4 \hat{j} + 4 \hat{k}$

D) $- 14 \hat{i} + 34 \hat{j} - 16 \hat{k}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] $\vec{τ} = \vec{r} \times \vec{F} = (7 \hat{i} + 3 \hat{j} + \hat{k}) (- 3 \hat{i} + \hat{j} + 5 \hat{k})$

$\vec{τ} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 7 & 3 & 1 \\ - 3 & 1 & 5 \end{matrix} | = 14 \hat{i} - 38 \hat{j} + 16 \hat{k}$

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