A circular disc D1 of 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 (as shown in figure). The moment of inertia of the system about the axis OO', passing through the centre of D1, as shown in the figure, will be

Engineering

Physics

Moment of Inertia

Question

A circular disc D₁ of 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 (as shown in figure). The moment of inertia of the system about the axis OO', passing through the centre of D₁, as shown in the figure, will be

$\frac{4}{5}$ MR²

3MR²

$\frac{2}{3}$ MR²

MR²

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

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