Q138 / 150 · MHT CET 2020 (20 Oct Shift 1) · Physics

Two circular rings 'A' and 'B' of radii 'nR' and 'R' are made from the same wire. The moment of inertia of 'A' about an axis passing through the centre and perpendicular to the plane of 'A' is 64 times that of the ring 'B'. The value of ' $n$ ' is

A
8
B
3
C
6
Correct answer
D
4

Solution

$\frac{\mathrm{I}_{\mathrm{A}}}{\mathrm{I}_{\mathrm{B}}}=\frac{64}{1}$ $64=\frac{m_{A} r_{A}^{2}}{m_{B} r_{B}^{2}}=\frac{2 \pi r_{A}}{2 \pi r_{B}} \frac{r_{A}^{2}}{r_{B}^{2}}=\frac{r_{A}^{3}}{r_{B}^{3}}=n^{3}$ $\therefore n=4$

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

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