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For identical discs each of mass $\mathrm{m}$ and radius $\mathrm{R}$ are placed in contract as shown in figure. Find MI of the system about an axis passing through $\mathrm{P}$ and Perpendicular to the plane of the figure.

Option: 1
$\mathrm{18 m R^2}$

Option: 2
$\mathrm{16 \mathrm{mR}^2}$

Option: 3
$\mathrm{10 m R^2}$

Option: 4
$\mathrm{10 \mathrm{m} R^2}$

Answers (1)

best_answer

MI of the system about CM axis and perpendicular to it-

$\mathrm{ I_{C M}=4\left[\frac{m R^2}{2}+m(\sqrt{2R})^2\right] }$

$\mathrm{ I_{C M}=4\left[\frac{m R^2}{2}+2 m R^2\right] \Rightarrow 4\left[\frac{m R^2+4 m R^2}{2}\right] }$

$\mathrm{ I_{C M}=10 m R^2 }$

Now, $\mathrm{I_p =I_{C M}+m d^2 }$

$\mathrm{ =10 m R^2+4 m(\sqrt{2} R)^2 }$

$\mathrm{ =10 m R^2+8 m R^2 }$

$\mathrm{ I_p =18 m R^2 }$

Hence option 1 is correct.

Posted by

jitender.kumar

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