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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
A triangular plate is shown. A force $\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }$ is applied at point $P$. The torque at point $P$ with respect to point $'O'$ and $'Q'$ are
  • ✓
    $-15-20 \sqrt{3}, 15-20 \sqrt{3}$
  • B
    $15+20 \sqrt{3}, 15-20 \sqrt{3}$
  • C
    $15-20 \sqrt{3}, 15+20 \sqrt{3}$
  • D
    $-15+20 \sqrt{3}, 15+20 \sqrt{3}$
✓

Answer

Correct option: A.
$-15-20 \sqrt{3}, 15-20 \sqrt{3}$
a
$\overrightarrow{ F }=4 \hat{ i }-3 \hat{ j }$

$\overrightarrow{ r }_{1}=5 \hat{ i }+5 \sqrt{3} \hat{ j } \& \overrightarrow{ r }_{2}=-5 \hat{ i }+5 \sqrt{3} \hat{j}$

Torque about $'O'$

$\vec{\tau}_{0}=\overrightarrow{ r }_{1} \times \overrightarrow{ F }=(-15-20 \sqrt{3}) \hat{ k }=(15+20 \sqrt{3})(-\hat{ k })$

Torque about $'Q'$

$\vec{\tau}_{Q}=\overrightarrow{ r }_{2} \times \overrightarrow{ F }=(-15+20 \sqrt{3}) \hat{ k }=(15-20 \sqrt{3})(-\hat{ k })$

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