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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
If force $\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}$ acts on a particle having position vector $2 \hat{i}+\hat{j}+2 \hat{k}$ then, the torque about the origin will be
  • A
    $3 \hat{ i }+4 \hat{ j }-2 \hat{ k }$
  • ✓
    $-10 \hat{ i }+10 \hat{ j }+5 \hat{ k }$
  • C
    $10 \hat{ i }+5 \hat{ j }-10 \hat{ k }$
  • D
    $10 \hat{ i }+\hat{ j }-5 \hat{ k }$
✓

Answer

Correct option: B.
$-10 \hat{ i }+10 \hat{ j }+5 \hat{ k }$
b
$\vec{\tau}=\vec{r} \times \vec{F}$

$=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & 2 \\ 3 & 4 & -2\end{array}\right|$

$=\hat{\hat{i}}(-2-8)-\hat{ j }(-4-6)+\hat{ k }(8-3)$

$=-10 \hat{ i }+10 \hat{ j }+5 \hat{ k }$

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