Question 429: Centre of Mass and Rotational Motion

Question

Two discs of same mass and different radii are made of different materials such that their

thicknesses are $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$ respectively. The densities of materials are in the ratio $3: 5$. The

moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The

value of $x$ is ________.

Accepted Answer

$m=ho \pi R^{2} t$
$$
\begin{aligned}
& 	ext { so } R^{2}=\frac{m}{ho \pi t} \\
& I=\frac{m R^{2}}{4}=\frac{m^{2}}{4 ho \pi t}
\end{aligned}
$$
So $\frac{I_{1}}{I_{2}}=\frac{ho_{2} t_{2}}{ho_{1} t_{1}}=\frac{5}{3} 	imes \frac{0.5}{1}=\frac{5}{6}$
So $x=5$

Centre of Mass and Rotational Motion

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