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A circular disc D₁of mass M and radius R has two identical discs D₂ and D₃ of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of interia of the system about the axis OO^', passing through the centre of D₁, as shown in the figure, will be:

Option 1)
3MR²
Option 2)

$\frac{2}{3}MR^{2}$
Option 3)

MR²
Option 4)

$\frac{4}{5}MR^{2}$

Answers (1)

best_answer

Paraller Axis Theorem -

$I_{b\: b'}=I_{a\: a'}+Mh^{2}$

- wherein

$b\: b'$ is axis parallel to $a\: a'$ & $a\: a'$ an axis passing through centre of mass.

$I=I_{1}+I_{2}+I_{3}$

$I_{1}=M.O.I$ of $D_{1}$ about ${00}'$

$=\frac{MR^{2}}{2}$

$I_{2}=M.O.I$ of $D_{3}$ about ${00}'$

$I_{2}=I_{3}\Rightarrow$ due to symmetry

$I_{2}=\left ( \frac{MR^{2}}{4} +MR^{2}\right )$

$I=I_{1}+2I_{2}$

$=\frac{MR^{2}}{2}+2\left ( \frac{MR^{2}}{4}+MR^{2} \right )$

$I=\frac{MR^{2}}{2}+2\times \frac{5MR^{2}}{4}$

$I=\frac{6MR^{2}}{2}$

$I=3MR^{2}$

Option 1)
3MR²
Option 2)

$\frac{2}{3}MR^{2}$

Option 3)

MR²

Option 4)

$\frac{4}{5}MR^{2}$

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