Three uniform circular discs, each of mass 0.5 kg and radius 10 cm , are kept in contact with each other as shown in the figure. Find the moment of inertia of the system when it rotates about the axis AB

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$2.5 \times 10^{- 2} {kgm}^{2}$

$1.375 \times 10^{- 2} {kgm}^{2}$

$2.3 \times 10^{- 3} {kgm}^{2}$

$1.375 \times 10^{- 3} {kgm}^{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} I = I_{1} + I_{2} + I_{3} \\ I = \frac{5 {MR}^{2}}{4} + \frac{5 {MR}^{2}}{4} + \frac{{MR}^{2}}{4} \end{array}$
$\begin{array}{l} I = \frac{11 {MR}^{2}}{4} \\ M = 0 .5 kg, r = 10 cm = 10 \times 10^{- 2} m \\ I = \frac{11 {MR}^{2}}{4} = \frac{11 \times 0 .5 \times (0 .1)^{2}}{4} \\ = 1 .375 \times 10^{- 2} {kgm}^{2} \end{array}$