The ratio of masses and radii of two circular | vedclass

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Question

(B) The moment of inertia $I$ of a circular ring about its central axis is given by the formula $I = MR^2$,where $M$ is the mass and $R$ is the radius

Vedclass · Accepted Answer

$2 : 1$

Vedclass · Answer

(B) The moment of inertia $I$ of a circular ring about its central axis is given by the formula $I = MR^2$,where $M$ is the mass and $R$ is the radius of the ring.Let the masses be $M_1$ and $M_2$,and the radii be $R_1$ and $R_2$.Given: $\frac{M_1}{M_2} = \frac{1}{2}$ and $\frac{R_1}{R_2} = \frac{2}{1}$.The ratio of moments of inertia is $\frac{I_1}{I_2} = \frac{M_1 R_1^2}{M_2 R_2^2}$.Substituting the given values: $\frac{I_1}{I_2} = \left( \frac{M_1}{M_2} ight) 	imes \left( \frac{R_1}{R_2} ight)^2$.$\frac{I_1}{I_2} = \left( \frac{1}{2} ight) 	imes \left( \frac{2}{1} ight)^2 = \frac{1}{2} 	imes 4 = 2$.Thus,the ratio is $2 : 1$.

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

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