JEE MAIN - Physics (2022 - 28th July Morning Shift - No. 24)
Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $$\mathrm{OO}^{\prime}$$ is $$\frac{x}{4} \,\mathrm{Ma}^{2}$$. Then, the value of $$x$$ will be ____________.
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Answer
3
Explanation
$$I = 2 \times \left( {{{M{{\left( {{a \over 2}} \right)}^2}} \over 4}} \right) + 2 \times \left( {{{M{{\left( {{a \over 2}} \right)}^2}} \over 4} + M{{\left( {{a \over 2}} \right)}^2}} \right)$$
$$ = {{M{a^2}} \over 8} + {{5M{a^2}} \over 8}$$
$$ = {{6M{a^2}} \over 8} = {3 \over 4}M{a^2}$$
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