A circular disc X of radius R is made from an iron pole of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness (t/4). then the relation between the moment of inertia IX and IY is

Question

A circular disc X of radius R is made from an iron pole of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness (t/4). then the relation between the moment of inertia IX and IY is (A) Iy=32Ix (B) Iy=16Ix (C) Iy=32 Ix (D) Iy=64 Ix

Tardigrade Admin · Accepted Answer

If t is the thickness and R is the radius of the disc, then mass

= π R^{2} tρ

ρ =

density of the material of the disc.
Moment of inertia of disc X,

I_{x} = \frac{1}{2} π R^{4} tρ ... (i)

Moment of inertia of disc Y,

I_{y} = 32 π R^{4} tρ ... (ii)

From equation

(i)

and

(ii)

I_{y} = 64 I_{x}

Q. A circular disc $X$ of radius $R$ is made from an iron pole of thickness $t$ , and another disc Y of radius $4 R$ is made from an iron plate of thickness $\frac{t}{4}$ . then the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is

$I_{y} = 32 I_{x}$

$I_{y} = 16 I_{x}$

$I_{y} = 32 I_{x}$

$I_{y} = 64 I_{x}$

Q. A circular disc X of radius R is made from an iron pole of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness 4t​. then the relation between the moment of inertia IX​ and IY​ is

Iy​=32Ix​

Iy​=16Ix​

Iy​=32Ix​

Iy​=64Ix​

If t is the thickness and R is the radius of the disc, then mass =πR2tρ ρ= density of the material of the disc. Moment of inertia of disc X, Ix​=21​πR4tρ...(i) Moment of inertia of disc Y, Iy​=32πR4tρ...(ii) From equation (i) and (ii) Iy​=64Ix​

Q. A circular disc $X$ of radius $R$ is made from an iron pole of thickness $t$ , and another disc Y of radius $4 R$ is made from an iron plate of thickness $\frac{t}{4}$ . then the relation between the moment of inertia $I_{X}$ and $I_{Y}$ is

$I_{y} = 32 I_{x}$

$I_{y} = 16 I_{x}$

$I_{y} = 32 I_{x}$

$I_{y} = 64 I_{x}$