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3-2.Motion in Plane
medium
The linear velocity of a rotating body is given by $\overrightarrow v = \overrightarrow \omega \times \overrightarrow r ,$where $\overrightarrow \omega $ is the angular velocity and $\overrightarrow r $ is the radius vector. The angular velocity of a body is $\overrightarrow \omega = \hat i - 2\hat j + 2\hat k$ and the radius vector $\overrightarrow r = 4\hat j - 3\hat k,$ then $|\overrightarrow v |$ is
A$\sqrt {29} $units
B$\sqrt {31} $units
C$\sqrt {37} $units
D$\sqrt {41} $units
Solution
(a) $\vec v = \vec \omega \times \vec r$
$ = \left|{\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\1&{ – 2}&2\\0&4&{ – 3}\end{array}} \right| = \hat i(6 – 8) – \hat j( – 3) + 4\hat k$
$ – 2\vec i + 3\vec j + 4\vec k$
$|\vec v|\; = \;\sqrt {{{( – 2)}^2} + {{(3)}^2} + {4^2}} $$ = \sqrt {29} \;unit$
$ = \left|{\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\1&{ – 2}&2\\0&4&{ – 3}\end{array}} \right| = \hat i(6 – 8) – \hat j( – 3) + 4\hat k$
$ – 2\vec i + 3\vec j + 4\vec k$
$|\vec v|\; = \;\sqrt {{{( – 2)}^2} + {{(3)}^2} + {4^2}} $$ = \sqrt {29} \;unit$
Standard 11
Physics
