Question

19. A metallic ring of mass 1 kg has moment

of inertia 1 kg m2

when rotating about

one of its diameters. It is molten and

remoulded into a thin uniform disc of the

same radius. How much will its moment

of inertia be, when rotated about its own

axis.

[Ans: 1 kg m2

]​

Answer 1

Answer:

Ans 1 kg m2

Explanation:

because because when it is rotated about its own axis its answer is 1 kg square

Answer 2

Answer:

1 kg m2

Explanation:

Given data :-

mass of ring and disc is M =1 kg

Moment of inertia of ring at diameter ( Ir )d = 1 kg m2

 Rr = Rd  

What we have to find out:-

Moment of inertia of disc about own axis = Id = ?

Solution:-

 Using theorem of perpendicular axes, for a ring M.I about its axis passing through C.M and perpendicular to its plane is twice the M.I about its any diameter, which is given by,  

 ( Ir )c = 2 ( Ir )d  

 = 2 * 1  

MRr2 = 2 kg m2  

Rr2  = Rd2  = 2 meter

Hence ,

Moment of inertia of disc about own axis is given by,

 Id   = ½ MRd2

      = ½ * 1* 2

   Id  = 1 kg m2