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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
What is the value of linear velocity, if  $\vec \omega \, = \,3\hat i\, - \,4\hat j\, + \hat k\,\,$  and  $\,\,\vec r \, = \,5\hat i\, - \,6\hat j\, + 6\hat k$
  • A
    $6\hat i\, + \,2\hat j\, - 3\hat k$
  • ✓
    $-18\hat i\, - \,13\hat j\, + 2\hat k$
  • C
    $4\hat i\, - \,13\hat j\, + 6\hat k$
  • D
    $6\hat i\, - \,2\hat j\, + 8\hat k$
✓

Answer

Correct option: B.
$-18\hat i\, - \,13\hat j\, + 2\hat k$
b
$\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{\omega}} \times \overrightarrow{\mathrm{r}}=\left|\begin{array}{ccc}{\hat{\mathrm{i}}} & {\hat{\mathrm{j}}} & {\hat{\mathrm{k}}} \\ {3} & {-4} & {1} \\ {5} & {-6} & {6}\end{array}\right|=-18 \hat{\mathrm{i}}-13 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$

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