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Q.

Four identical discs each of mass ‘M’ and diameter ‘a’ are arranged in a small plane as shown in figure. If the moment of inertia of the system about OO' is $\frac{x}{4}$ Ma². Then, the value of x will be _______.

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answer is 3.

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Detailed Solution

$\begin{array}{l} I = 2 \times (\frac{M {(\frac{a}{2})}^{2}}{4}) + 2 \times (\frac{M {(\frac{a}{2})}^{2}}{4} + M {(\frac{a}{2})}^{2}) \\ = \frac{{Ma}^{2}}{8} + \frac{5 {Ma}^{2}}{8} \\ = \frac{6 {Ma}^{2}}{8} = \frac{3}{4} {Ma}^{2} \end{array}$

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