SATHEE: Motion in a Plane - Result Question 16

Motion in a Plane - Result Question 16

18. 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]

(a) $- 21 \hat{i} + 3 \hat{j} + 5 \hat{k}$

(b) $- 14 \hat{i} + 3 \hat{j} + 16 \hat{k}$

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

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Answer:

Correct Answer: 18. (d)

Solution:

(d) $\vec{F} = - 3 \hat{i} + \hat{j} + 5 \hat{k}; \vec{r} = 7 \hat{i} + 3 \hat{j} + \hat{k}$

Torque $(\vec{τ}) = \vec{r} \times \vec{F}$

$= (7 \hat{i} + 3 \hat{j} + \hat{k}) \times (- 3 \hat{i} + \hat{j} + 5 \hat{k})$

$= 7 \hat{k} + 35 (- \hat{j}) - 9 (- \hat{k}) + 15 \hat{i} - 3 \hat{j} + (- \hat{i})$

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

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Motion in a Plane - Result Question 16

18. Find the torque of a force F→=−3i^+j^+5k^ acting at the point r→=7i^+3j^+k^.

Answer:

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