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Two rings of radii R and nR made from the same wire have the ratio of moments of inertia about an axis passing through their centre equal to 1:8. What is the value of n?

(a) 2

(b) 2√2

(c) 4

(d) ½

The question was posed to me in homework.

This key question is from Significance of Moment of Inertia in division Laws of Motion of Engineering Physics I

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The correct answer is (a) 2

To explain: As the radius of the second ring is n times, length and hence the mass of wire used is also n times.

I1/I2 = (MR^2)/(nM(nR)^2)=1/n^3 = 1/8

Therefore, n=2.

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