Verified Solution • 2025–26 Session moderate

QJEEM22Ph4529: JEE Main 2022 Physics - Class 11 JEEM22Ph4529 Solution: The moment of inertia of a uniform thin rod about a…

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If I1I2{{{I_1}} \over {{I_2}}} is xπ23{{x{\pi ^2}} \over 3} , then the value of x will be ____________.

Step-by-Step Verified Solution

I1=ML23{I_1} = {{M{L^2}} \over 3} ..... (1)

For ring : I2=MR22{I_2} = {{M{R^2}} \over 2}

and 2πR=L2\pi R = L

⇒I2=M2(L24π2)\Rightarrow {I_2} = {M \over 2}\left( {{{{L^2}} \over {4{\pi ^2}}}} \right) ...... (2)

⇒I1I2=8π23\Rightarrow {{{I_1}} \over {{I_2}}} = {{8{\pi ^2}} \over 3}

⇒x=8\Rightarrow x = 8

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