Four identical small beads

PHYSICS · Single correct · A Level · Physics · Engineering physics · Engineering physics

Problem

Four identical small beads, each of mass

m

, can slide without friction on a light rigid wire of length

2L

. The wire is mounted so it can rotate in a horizontal plane about an axis through its midpoint and perpendicular to the wire. Three different configurations are prepared: • Configuration A: two beads are fixed at the ends of the wire; the other two are removed. • Configuration B: two beads are fixed at the quarter-length points (

\frac{L}{2}

from the center on each side); the other two are removed. • Configuration C: one bead is fixed at the center and one bead is fixed at one end; the other two are removed. Neglect the mass of the wire. Which ranking correctly orders the rotational inertias

I_A, I_B,

and

I_C

of the three configurations about the given axis, from greatest to least? (a)

I_A > I_B > I_C

(b)

I_B > I_A > I_C

(c)

I_A > I_C > I_B

(d)

I_C > I_A > I_B

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