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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 moment of inertia of a square sheet of side $l$ and mass per unit area $\mu $ about an axis passing through the centre and perpendicular to its plane
  • A
    $\frac{{\mu {l^2}}}{{12}}$
  • B
    $\frac{{\mu {l^2}}}{6}$           
  • C
    $\frac{{\mu {l^4}}}{{12}}$
  • ✓
    $\frac{{\mu {l^4}}}{6}$
✓

Answer

Correct option: D.
$\frac{{\mu {l^4}}}{6}$
d
side $=l$

Mass per unit area $=$ $\mu$

Total mass $M=\mu l^{2}$

Now, the moment of inertia is $I=\frac{M R^{2}}{12}$

By perpendicular axis theorem $I=I_{x}+I_{y}$

$I=2 I_{x}$

$I=2 \times \frac{\mu l^{2} \times l^{2}}{12}$

$I=\frac{\mu l^{4}}{6}$

Hence, the moment of inertia of a square sheet is $\frac{\mu l^{4}}{6}$

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