"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 ${{{I_1}} \over {{I_2}}}$ is ${{x{\pi ^2}} \over 3}$, then the value of x will be ____________."

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Accepted Answer

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

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

and $2\pi R = L$

$\Rightarrow {I_2} = {M \over 2}\left( {{{{L^2}} \over {4{\pi ^2}}}} \right)$ ...... (2)

$\Rightarrow {{{I_1}} \over {{I_2}}} = {{8{\pi ^2}} \over 3}$

$\Rightarrow x = 8$

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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 ${{{I_1}} \over {{I_2}}}$ is ${{x{\pi ^2}} \over 3}$, then the value of x will be ____________.

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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 ${{{I_1}} \over {{I_2}}}$ is ${{x{\pi ^2}} \over 3}$, then the value of x will be ____________.

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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 ${{{I_1}} \over {{I_2}}}$ is ${{x{\pi ^2}} \over 3}$, then the value of x will be ____________.