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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
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $O$ (the centre of mass) and $O ^{\prime}($ corner point $)$ is 
  • A
    $1 / 2$
  • B
    $2 / 3$
  • C
    $1 / 8$
  • ✓
    $1 / 4$
✓

Answer

Correct option: D.
$1 / 4$
d
Rectangular sheet

$I _{ O }=\frac{ M }{12}\left[ L ^{2}+ B ^{2}\right]=\frac{ M }{12}\left[80^{2}+60^{2}\right]$

$I _{ O }= I _{0}+ Md ^{2}\{$ parallel axis theorem $\}$

$\quad=\frac{ M }{12}\left[80^{2}+60^{2}\right]+ M [50]^{2}$

$\frac{ I _{ O }}{ I _{ O }}=\frac{ M / 12\left[80^{2}+60^{2}\right]}{\frac{ M }{12}\left[80^{2}+60^{2}\right]+ M [50]^{2}}=\frac{1}{4}$

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