Question

Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as ;
$I _{1}=$ M.I. of thin circular ring about its diameter.
$I _{2}=$ M.I. of circular disc about an axis perpendicular to the disc and going through the centre,
$I_{3}=$ M.I. of solid cylinder about its axis and
$I _{4}=$ M.I. of solid sphere about its diameter. Then :

• A. $I _{1}+ I _{3}< I _{2}+ I _{4}$
• B. $I _{1}+ I _{2}= I _{3}+\frac{5}{2} I _{4}$
• C. $I _{1}= I _{2}= I _{3}> I _{4}$
• D. $I _{1}= I _{2}= I _{3}< I _{4}$

Answer 1

Answer: (C)

Ring $I_{1}=\frac{M R^{2}}{2}$ about diameter
Disc $I_{2}=\frac{M R^{2}}{2}$
Solid cylinder $I_{3}=\frac{M R^{2}}{2}$
Solid sphere $I_{4}=\frac{2}{5} M R^{2}$
$I_{1}=I_{2}=I_{3}>I_{4}$