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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 force $F\, = 2.0\,N$ acts on a particle $P$ in the $xz-$ plane. The force $F$ is parallel to $x-$ axis. The particle $P$ (as shown in the figure) is at a distance $3\,m$ and the line joining $P$ with the origin make angle $30^o$ with the $x-$ axis. The magnitude of torque on $P$ with respect to origin $O(in N-m)$ is
  • A
    $2$
  • ✓
    $3$
  • C
    $4$
  • D
    $5$
✓

Answer

Correct option: B.
$3$
b
Torque, $\quad \vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}$

In magnitude, $\mathrm{t}=\mathrm{rF} \sin \theta$

Where $\theta$ is the angle between $\overrightarrow{\mathrm{r}}$ and $\overrightarrow{\mathrm{F}}$.

Here, $F=2.0 \mathrm{N}, \mathrm{r}=3 \mathrm{m}, \theta=30^{\circ}$

The magnitude of torque on $P$ with respect to origin $\mathrm{O}$ is

$\tau=(3 m)(2.0 \mathrm{N}) \sin 30^{\circ}=(3 \mathrm{m})(2.0 \mathrm{N})\left(\frac{1}{2}\right)=3 \mathrm{Nm}$

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