Question

iv) In a certain unit, the radius of gyrati
of a uniform disc about its central a
transverse axis is V2.5. Its radius
gyration about a tangent in its plane
the same unit) 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 .

Explanation:

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