Question

Two discs of same mass and same thickness have densities as 17g/cm³ and 51g/cm³. The ratio of their moment of inertia about their central axes is
(A) 1/3
(B) 2/3
(C) 3/1
(D) 3/2​

Answer 1

Answer:

(C) is the correct option

Explanation:

the moment of inertia of a circular disc about the axis passing through the centre of mass is MR²/2 where M is the mass of the disc and R is the radius of the disc..

let the mass and thickness be m and h respectively

given:

for 1st ringdensity=17 g/cm³

mass/volume=17 g/cm³

m/π(R1)²h=17 g/cm³ ......equ(i)

similarly, for 2nd ring

m/π(R2)²h=51 g/cm³.....equ(ii)

on dividing equ(ii) by equ(i)

we get

(R1)²/(R2)²=3/1

now the ratio of their moment of inertia about central axis=

m(R1)²/2 ÷ m(R2)²/2

=>(R1)²/(R2)²=3/1

thus,the ratio of their moment of inertia is 3:1.

Answer 2

Answer:

Answer:

(C) is the correct option

Explanation:

the moment of inertia of a circular disc about the axis passing through the centre of mass is MR²/2 where M is the mass of the disc and R is the radius of the disc..

let the mass and thickness be m and h respectively

given:

for 1st ringdensity=17 g/cm³

mass/volume=17 g/cm³

m/π(R1)²h=17 g/cm³ ..equ(i)

similarly, for 2nd ring

m/π(R2)²h=51 g/cm³..equ(ii)

on dividing equ(ii) by equ(i)

we get

(R1)²/(R2)²=3/1

now the ratio of their moment of inertia about central axis=

m(R1)²/2 ÷ m(R2)²/2

=>(R1)²/(R2)²=3/1

thus,the ratio of their moment of inertia is 3:1.

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