SATHEE: Kinematics Question 260

Kinematics Question 260

Question: The torque of the force $\vec{F} = (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) N$ acting at the point $\vec{r} = (3 \hat{i} + 2 \hat{j} + 3 \hat{k})$ m about the origin be [CBSE PMT 1995]

Options:

A) $6 \hat{i} - 6 \hat{j} + 12 \hat{k}$

B) $17 \hat{i} - 6 \hat{j} - 13 \hat{k}$

C) $- 6 \hat{i} + 6 \hat{j} - 12 \hat{k}$

D) $- 17 \hat{i} + 6 \hat{j} + 13 \hat{k}$

Show Answer

Answer:

Correct Answer: B

Solution:

$\vec{τ} = \vec{r} \times \vec{F}$

$= | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 3 \\ 2 & - 3 & 4 \end{matrix} |$

$= [(2 \times 4) - (3 \times - 3)] \hat{i} + [(2 \times 3) - (3 \times 4)] \hat{j}$

$+ [(3 \times - 3) - (2 \times 2)] \hat{k}$

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

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Kinematics Question 260

Question: The torque of the force F→=(2i^−3j^+4k^)N acting at the point r→=(3i^+2j^+3k^) m about the origin be [CBSE PMT 1995]

Options:

Answer:

Solution:

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Question: The torque of the force $\vec{F} = (2 \hat{i} - 3 \hat{j} + 4 \hat{k}) N$ acting at the point $\vec{r} = (3 \hat{i} + 2 \hat{j} + 3 \hat{k})$ m about the origin be [CBSE PMT 1995]