A circular disc is made using iron and alumin | vedclass

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

Question

(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed total mass, the mas

Vedclass · Accepted Answer

The inner part should be made of aluminum and the outer part of iron.

Vedclass · Answer

(B) The moment of inertia $I$ of a body about an axis is given by $I = \int r^2 dm$. To maximize the moment of inertia for a fixed total mass, the mass should be distributed as far as possible from the axis of rotation. Since the density of iron $(\rho \approx 7870 \ kg/m^3)$ is significantly higher than that of aluminum $(\rho \approx 2700 \ kg/m^3)$, placing the denser material (iron) at the outer rim increases the moment of inertia compared to placing it at the center. Therefore, the inner part should be aluminum and the outer part should be iron.

$A$ circular disc is made using iron and aluminum such that its moment of inertia about its geometric axis is maximum. For this to happen:

Similar Questions

$A$ thin rod of mass $M$ and length $L$ is bent at its midpoint $A$ such that it forms an angle of $60^{\circ}$. What is the moment of inertia about an axis passing through the midpoint $A$ and perpendicular to the plane of the rod?

An iron circular disc $X$ has radius $R$ and thickness $t$. Another iron circular disc $Y$ has radius $4R$ and thickness $t/4$. The relationship between the moments of inertia $I_X$ and $I_Y$ of these two discs is .......

Write the practical uses of moment of inertia.

Two solid spheres of iron have radii in the ratio $1 : 2$. Their moments of inertia will be in the ratio

Three identical thin rods each of mass $m$ and length $l$ are placed along $x, y$ and $z$-axes respectively. They are placed such that one end of each rod is at the origin $O$. The moment of inertia of this system about the $z$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module