Question 468: Centre of Mass and Rotational Motion

Question

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 _______.

Accepted Answer

$$\overrightarrow 	au   = \overrightarrow r  	imes F = (3\widehat i + \widehat j - 2\widehat k) 	imes (\widehat i + 2\widehat j + 3\widehat k)$$
$$ = \left| {\matrix{
   i & j & k  \cr 
   3 & 1 & { - 2}  \cr 
   1 & 2 & 3  \cr

} } ight|$$
$$ = \widehat i(3 + 4) - \widehat j(9 + 2) + \widehat k(6 - 1)$$
$$\overrightarrow 	au   = 7\widehat j - 11\widehat j + 5\widehat k$$
$$\left| {\overrightarrow 	au  } ight| = \sqrt {49 + 121 + 25}  = \sqrt {195} $$
$$ 	herefore $$ $$x = 195$$

Centre of Mass and Rotational Motion

Integer / Numeric Answer Type