Question

Two circular dises have their masses
in the ratio 1:2 and their diameter
in the ratio 2:1 what is the ratio
of their moment of inertia.​

Answer 1

Explanation:

$\frac{m1}{m2} = \frac{1}{2} \\ \frac{d1}{d2} = \frac{2}{1} \\ = > \frac{2r1}{2r2} = \frac{2}{1} \\ = > \frac{r1}{r2} = \frac{2}{1} \\ \\ as \: we \: know \: that \: momentof \: inertia \\ of \: disc \: \: \: \: i = \frac{m {r}^{2} }{2} \\ \\ \frac{i1}{i2} = \frac{ \frac{m1 {r1}^{2} }{2} }{ \frac{m {r2}^{2} }{2} } \\ = > \frac{i1}{i2} = \frac{m1}{m2} \times \frac{ {r1}^{2} }{ {r2}^{2} } \\ = \frac{1}{2} \times \frac{ {2}^{2} }{ {1}^{2} } \\ = \frac{1}{2} \times \frac{4}{1 } \\ = 2$