Question

If a circular concentric hole is made in a disc, then about an axis passing through the centre of the disc and perpendicular to its plane then the:

• A. Radius of gyration increases
• B. Radius of gyration decreases
• C. Moment of inertia increases
• D. Moment of inertia decreases

Answer 1

The correct option is C Moment of inertia increases

$d\in =Bxwdx$

$\in ={\int }_0^{l}Bxwdx$

$=Bw{\int }_0^{l}x.dx=Bw[\frac{x^2}{2}{]}_0^l$

$\in =Bw\frac{l^2}{2}$

$\in =\frac{1}{2}Bw{l}^2$