Question

(i)
The moment of Inertia of a Uniform Disc about its central and
transverse axis 8 kg-m’ then the moment of Inertia of a Uniform
Disc about an axis coincide with its diameter is...
(a) 2 kg-m?
(b) 16 kg-m
(c) 4 kg-m
(d) 8 kg-m?​

Answer 1

The moment of inertia about an axis coincide with its diameter is 4 kgm². so option (c) is correct.

The moment of inertia of a uniform disc about its central and transverse axis 8 kgm².

We have to find the moment of inertia of the disc about an axis coincide with its diameter.

Moment of inertia of disc about an axis passing through its centre and perpendicular to its plane or moment of inertia of disc about transverse axis is given by,

$\quad I_z=\frac{MR^2}{2}$

here,

$I_z=8kgm^2$ ...(1)

from perpendicular axis theorem,

$I_z=I_x+I_y$

but,

$I_x=I_y$

$\text{so,} I_x=I_y=\frac{I_z}{2}$

from equation (1),

$I_x=I_y=\frac{8}{2}=4kgm^2$

hence, the moment of inertia about an axis coincide with its diameter is 4 kgm².