Question

The ratio of the masses of two thin uniform circular discs made of same material having same thickness is 4:9. The ratio of the moments of inertia of the two discs about their diameters is

• A. 1:1
• B. 2:3
• C. 4:9
• D. 16:81

Hint:

Always use correct axis formula. For thin discs about diameter, $I = \frac{1}{4} M R^2$, check if radius scales with mass or not.

Answer 1

The Correct Option is A

1. Moment of inertia of thin disc about diameter: $I = \frac{1}{4} M R^2$.
2. Masses given $M_1:M_2 = 4:9$. Radii same (thickness same, same material).
3. So $I_1/I_2 = (\frac{1}{4} M_1 R^2) / (\frac{1}{4} M_2 R^2) = M_1/M_2 = 4/9$? Wait – check: diameters – for thin discs about **diameter**, $I \propto MR^2$, but if **discs have same area ratio as mass**, ratio of $R^2$ cancels mass effect. Hence ratio is 1:1.