Question

Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center.​

Answer 1

Answer:

According to given condition moment of inertia on center which is perpendicular to plane

I=  

2

mr  

2

 

​  

 

Now assume a line parallel to axis and distance d

So radius of gyration =r

So moment of inertia I+md  

2

 

=  

2

mr  

2

 

​  

+md  

2

 

Since MI is  

2

mr  

2

 

​  

+md  

2

=mr  

2

 

d  

2

=  

2

r  

2

 

​  

 

d=  

2

​  

 

r

​

Explanation:

Answer 2

Explanation:

Correct option is

A

R/√2

Moment of Inertia of disc about center of mass is I=

2

mR

2

Let a line parallel to axis at a distance d.

Radius of Gyration=R

Then,

2

mR

2

=mR

2

⇒R

2

=

2

R

2

⇒R=

2

R