The force 7 i + 3 j - 5 k acts on a particle whose position vecto… - Vidyadip

MCQ

The force $7\widehat i + 3\widehat j - 5\widehat k$ acts on a particle whose position vector is $\widehat i - \widehat j + \widehat k$ . What is the torque of the given force about the origin ?

✓
$2 \widehat i +12\widehat j +10\widehat k$
B
$2\widehat i +10\widehat j +12\widehat k$
C
$2\widehat i +10\widehat j +10\widehat k$
D
$10\widehat i + 2\widehat j + \widehat k$

✓

Answer

Correct option: A.

$2 \widehat i +12\widehat j +10\widehat k$

a
Here, $\vec{r}=\hat{i}-\hat{j}+\hat{k}$

$\overrightarrow{\mathrm{F}}=7 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}$

Torque, $\vec{\tau}=\vec{r} \times \vec{F}$

$\vec{\tau}=\left|\begin{array}{rrr}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {1} & {-1} & {1} \\ {7} & {3} & {-5}\end{array}\right|=\hat{i}(5-3)+\hat{j}(7-(-5))+\hat{k}(3-(-7))$

or $\vec{\tau}=2 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}$

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