Two discs of same mass and same thickness hav | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The moment of inertia of a disc is $I = \frac{1}{2} M r^2$.Since mass $M = V \rho = (\pi r^2 t) \rho$,we can write $r^2 = \frac{M}{\pi t \rho}$.Su

Vedclass · Accepted Answer

$\rho_2 : \rho_1$

Vedclass · Answer

(D) The moment of inertia of a disc is $I = \frac{1}{2} M r^2$.Since mass $M = V \rho = (\pi r^2 t) \rho$,we can write $r^2 = \frac{M}{\pi t \rho}$.Substituting $r^2$ into the moment of inertia formula: $I = \frac{1}{2} M \left( \frac{M}{\pi t \rho} \right) = \frac{M^2}{2 \pi t \rho}$.Given that both discs have the same mass $M$ and same thickness $t$,the moment of inertia is inversely proportional to the density: $I \propto \frac{1}{\rho}$.Therefore,the ratio of their moments of inertia is $\frac{I_1}{I_2} = \frac{\rho_2}{\rho_1}$.

Two discs of same mass and same thickness have densities $\rho_1$ and $\rho_2$. The ratio of their moment of inertia about their central axes is .........

Similar Questions

One solid sphere $A$ and another hollow sphere $B$ have the same mass and the same outer radii. Their moments of inertia about their diameters are $I_{A}$ and $I_{B}$ respectively. Which of the following relations is correct?

Which of the following has the largest moment of inertia?

The moment of inertia of a uniform rod of length $2l$ and mass $m$ about an axis $xx'$ passing through its centre and inclined at an angle $\alpha$ is

For a rectangle $ABCD$ with $BC = 2AB$,about which axis will the moment of inertia be minimum?

Vedclass Test Series

Exam Paper Generator

Online Exam Module