SATHEE: Rotational Motion Question 91

Rotational Motion Question 91

Question: The moment of the force, $\vec{F} =4 \hat{i} +5 \hat{j} -6 \hat{k}$ at (2, 0, -3), about the point (2, -2, -2), is given by

Options:

A) $-7 \hat{i} -8 \hat{j} -4 \hat{k}$

B) $-4 \hat{i} - \hat{j} -8 \hat{k}$

C) $-8 \hat{i} -4 \hat{j} -7 \hat{k}$

D) $-7 \hat{i} -4 \hat{j} -8 \hat{k}$

Show Answer

Answer:

Correct Answer: D

Solution:

[d]

$\vec{τ} = (\vec{r} - {\vec{r}}_{0}) \times \vec{F}$ (i)

$\vec{r} - {\vec{r}}_{_{0}} = (2 \hat{i} - 0 \hat{j} - 3 \hat{k}) - (2 \hat{i} - 2 \hat{j} - 2 \hat{k})$

$= 0 \hat{i} + 2 \hat{j} - \hat{k}$

$\vec{τ} = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & - 1 \\ 4 & 5 & - 6 \end{matrix} | = - 7 \hat{i} - 4 \hat{j} - 8 \hat{k}$

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