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QJEEM22Phfef7: JEE Main 2022 Physics - Class 11 JEEM22Phfef7 Solution: Four identical discs each of mass ' ' and diameter ' ' are…

Four identical discs each of mass ' M\mathrm{M} ' and diameter ' a\mathrm{a} ' are arranged in a small plane as shown in figure. If the moment of inertia of the system about OO′\mathrm{OO}^{\prime} is x4 Ma2\frac{x}{4} \,\mathrm{Ma}^{2} . Then, the value of xx will be ____________.

JEE Main 2022 (Online) 28th July Morning Shift Physics - Rotational Motion Question 60 English

Step-by-Step Verified Solution

I=2×(M(a2)24)+2×(M(a2)24+M(a2)2)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)

=Ma28+5Ma28= {{M{a^2}} \over 8} + {{5M{a^2}} \over 8}

=6Ma28=34Ma2= {{6M{a^2}} \over 8} = {3 \over 4}M{a^2}

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