A force $\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$ N acts at a point
$\left( {4\widehat i + 3\widehat j - \widehat k} \right)$ m. Then the magnitude of torque
about the point $\left( {\widehat i + 2\widehat j + \widehat k} \right)$ m will be $\sqrt x$ N m.
The value of x is _______.
Answer (integer)
195
Solution
$$\overrightarrow \tau = \overrightarrow r \times F = (3\widehat i + \widehat j - 2\widehat k) \times (\widehat i + 2\widehat j + 3\widehat k)$$<br><br>$$ = \left| {\matrix{
i & j & k \cr
3 & 1 & { - 2} \cr
1 & 2 & 3 \cr
} } \right|$$<br><br>$= \widehat i(3 + 4) - \widehat j(9 + 2) + \widehat k(6 - 1)$<br><br>$\overrightarrow \tau = 7\widehat j - 11\widehat j + 5\widehat k$<br><br>$\left| {\overrightarrow \tau } \right| = \sqrt {49 + 121 + 25} = \sqrt {195}$<br><br>$\therefore$ $x = 195$
About this question
Subject: Physics · Chapter: Rotational Motion · Topic: Centre of Mass
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