Figure shows particles each connected rigidly by massless thin rods. Mass of each particle is m . In each case calculate the moment of inertia of the assembly about the axis shown in the figure. List-

Question

Figure shows particles each connected rigidly by massless thin rods. Mass of each particle is $m$ . In each case calculate the moment of inertia of the assembly about the axis shown in the figure.

List-I	List-II
(P) Edge length of cube = L. Axis passing through centres of upper and lower faces.	$(1) 8 m L^{2}$
(Q) Edge length of cube = L. Axis passing through an edge of the cube.	$(2) 4 m L^{2}$
(R) Radius of cylinder = L. Axis passing through symmetry axis of cylinder.	$(3) 3 m L^{2}$
(S) Edge of tetrahedron = L. Axis passing through centroid of base.	$(4) m L^{2}$
	(5) None

TestHub · Accepted Answer

For point particles: I = ∑ m r ⊥ 2 ​ P: eight vertices at r ⊥ ​ = L / 2 ​ . I P ​ = 8 m ( 2 L 2 ​ ) = 4 m L 2 Q: two vertices on the axis; four at L , two at 2 ​ L . I Q ​ = 4 m L 2 + 2 m ( 2 L 2 ) = 8 m L 2 R: eight rim particles, each at distance L . I R ​ = 8 m L 2 S: top particle on the axis; three base vertices at L / 3 ​ . I S ​ = 3 m ( 3 L 2 ​ ) = m L 2 P to 2, Q to 1, R to 1, S to 4. Answer: C.

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