Question

From a disc of mass 2 kg and radius 4m a small disc of radius 1 m coinciding with center o is extracted. The new moment of inertia. About an axis passing through o perpendicular to plane of disc is

Answer 1

Answer:

15.9375 or 255/16

Explanation:

Refer to the material.

Answer 2

Answer:

15.93 Kgm^2.

Explanation:

We know that the mass of the disc is 2 kg and the radius is 4m from which a disc of radius 1 m is coinciding with the center O.

So, we can say that the M1/A1 = M2/A2 which is 2/π(R1)^2 = M2/π(R2)^2 which on solving we will get that M2 = 2(R2^2)/(R1)^2 or 2 *1/16 which is 1/8 kg.

So, the total moment of inertia will be moment of inertia of the original disc - the moment of inertia of the small disc.

Hence, 1/2M1R1^2 - 1/2 M2R2^2.

1/2(M1R1^2 - M2R2^2).  

Which on solving we get 1/2(2*4^2 - 1/8(1)^2). Which we will get as 255/16 or it can be written as 15.93 kgm^2.