Question

in a unit , the radius of gyration of a uniform disc about its central and transverse axis is underroot2. 5 .It's radius of gyration about a tangent in its plane must be​

Answer 1

Answer:

Given:

The radius of gyration of a uniform disc about its central and transverse axis =2.5 units

To Find :

The radius of gyration of the uniform disc about a tangent in its plane = ?

Solution :

Since we know that the moment of inertia disc about central transverse axis is given as :

Here m and R are mass and radius of disc respectively .

Let , K = radius of gyration

∴

So, = 2.5 units (radius of gyration is given 2.5 units )

Now by theorem of perpendicular axis :

Where and are the moment of inertia about x , y and z axis .

∴For a uniform disc ,

So,

Now by theorem of parallel axis :

Moment of inertia about tangent =

Let K' be the radius of gyration about the tangent , then :

So, K' =

Since units

So,

= units

Hence , (D) is the correct option i.e. radius of gyration about a tangent of the disc is units .