Question

For the same total mass which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body.
A. a disc of radius a
B. a ring of radius oa
C. a square lamina of side `2 a`
D. four rods forming a square of side `2a`.

Answer 1

Correct Answer - D
For Disc `I_("disc") = (1)/(2) ma^(2)`
For Ring `I_("ring") = ma^(2)`
For square lamine of side `2a = (1)/(6) m(2a)^(2) = (2)/(3) ma^(2)`

For Rods forming a square of side `2 a`
`I_("square") = 4[(m(2a)^(2))/(12) +ma^(2)] =4[(ma^(2))/(3)+ma^(2)] = (16 ma^(2))/(3)`.