Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

Question

Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter: (A) 1: 4 (B) 4: 1 (C) 1: 2 (D) 2: 1

Tardigrade Admin · Accepted Answer

Moment of inèrtia of ring I=m r2. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a027c3ea3594c334b208633e21262e14-.png" /> Moment of inertia of ring about diameter (from theorem of parallel axis) I1 =m r2+m r2=2 m r2 I: I2 =1: 2

Q. Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

1 : 4

4 : 1

1 : 2

2 : 1

Moment of inèrtia of ring $I = m r^{2}$ .

Moment of inertia of ring about diameter
(from theorem of parallel axis)
$I_{1} = m r^{2} + m r^{2} = 2 m r^{2}$
$I : I_{2} = 1 : 2$

Q. Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

1 : 4

4 : 1

1 : 2

2 : 1

Moment of inèrtia of ring I=mr2. Moment of inertia of ring about diameter (from theorem of parallel axis) I1​=mr2+mr2=2mr2 I:I2​=1:2

Moment of inèrtia of ring $I = m r^{2}$ .

Moment of inertia of ring about diameter
(from theorem of parallel axis)
$I_{1} = m r^{2} + m r^{2} = 2 m r^{2}$
$I : I_{2} = 1 : 2$