Two discs of same mass and same thickness (t) | vedclass

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

Question

(B) The moment of inertia of a disc of mass $M$ and radius $R$ about an axis passing through its centre and perpendicular to its plane is $I = \frac{1

Vedclass · Accepted Answer

$d_2 : d_1$

Vedclass · Answer

(B) The moment of inertia of a disc of mass $M$ and radius $R$ about an axis passing through its centre and perpendicular to its plane is $I = \frac{1}{2} M R^2$.Since the mass $M$ is the same for both discs,the ratio is $\frac{I_1}{I_2} = \frac{R_1^2}{R_2^2}$.The mass of a disc is given by $M = 	ext{Volume} 	imes 	ext{Density} = (\pi R^2 t) d$.Since $M$ and $t$ are constant,we have $R^2 \propto \frac{1}{d}$,which implies $R^2 d = 	ext{constant}$.Therefore,$R_1^2 d_1 = R_2^2 d_2$,which gives $\frac{R_1^2}{R_2^2} = \frac{d_2}{d_1}$.Substituting this into the ratio of moments of inertia,we get $\frac{I_1}{I_2} = \frac{d_2}{d_1}$.

Two discs of same mass and same thickness $(t)$ are made from two different materials of densities $d_1$ and $d_2$ respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of the two discs about an axis passing through the centre and perpendicular to the plane of the disc is:

Similar Questions

The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its center on the $x$-axis at a distance $a$ from the origin. Then,the moment of inertia of the disc about the $x$-axis is:

$A$ slender rod of mass $M$ and length $L$ is hinged at one end to swing freely in a vertical plane. Its density is non-uniform and varies linearly from the hinged end to the free end,doubling its value. The moment of inertia of the rod about the rotation axis passing through the hinge point is:

If a spherical planet of mass $M$ and radius $R$ suddenly shrinks to half its size,and its mass reduces to half,what is the new moment of inertia of the planet about its diameter?

Explain the radius of gyration.

$A$ thin rod of total length $4l$ and total mass $4M$ is bent into the shape shown in the figure. Each segment has length $l$ and mass $M$. What is the moment of inertia of the rod about the axis passing through point $O$ and perpendicular to the plane of the paper?

Vedclass Test Series

Exam Paper Generator

Online Exam Module