Q101 / 150 · MHT CET 2020 (14 Oct Shift 1) · Physics

Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane as $1: 8 .$ The value of 'n' is (mass per unit length is constant)

A
1
B
3
C
4
Correct answer
D
2

Solution

$\begin{array}{l} I_{1}=M R^{2}, I_{2}=(n M)(n R)^{2}=n^{3} m R^{2} \\ \therefore \frac{I_{1}}{I_{2}}=\frac{1}{n^{3}}=\frac{1}{8} \\ \therefore n=2 \end{array}$

Hence, the correct answer is option: 'D'.

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