Question

the moment of inertia of a circular ring of mass 1 kg about an Axis passing through its centre and perpendicular to its plane is 4 kg metre square to diameter of the Ring

Answer 1

Question :

The moment of inertia of a circular ring of mass 1 kg about an Axis passing through its centre and perpendicular to its plane is 4 kg metre square .Find diameter of the Ring.

Theory :

•Moment of Inertia

The virtue by which a body revolving around an Axis opposes the change in rotation motion is known as moment of inertia.

•Moment of inertia of ring about an Axis perpendicular to plane passing through centre of mass:

${\purple{\boxed{\large{\bold{I=Mr{}^{2}}}}}}$

Solution :

Given :

Mass of circular ring,M = 1kg

Moment of inertia of Ring,axis ( perpendicular to plane passing through centre of mass)= 4 kgm²

I =Mr²

put the values ;

$\implies4 = 1 \times r {}^{2}$

$\implies \: r = \frac{ + }{}2$

Since the radius cannot be negative

Thus, r = 2

Therefore diameter of ring = 4m

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More About Moment of Intertia:

1) moment of inertia depends upon :

•mass of the body

•mass distribution of body

•position of axis of rotation

•in shape ,size and density

2) SI unit is kg-m²

3) CGS unit is g-cm²

Answer 2

Follow the attachment ✌