Four rods of equal length ℓ and mass m each form a square as shown in figure. Moment of inertia about four axes 1, 2,3 and 4 are say I 1 , I 2 , I 3 and I 4 . List - I List - II (P) I 1 (1)

Question

Four rods of equal length ℓ and mass m each form a square as shown in figure. Moment of inertia about four axes 1, 2,3 and 4 are say I 1 ​ , I 2 ​ , I 3 ​ and I 4 ​ . List - I List - II (P) I 1 ​ (1) 3 4 ​ m ℓ 2 (Q) I 2 ​ (2) 3 2 ​ m ℓ 2 (R) I 3 ​ (3) 2 1 ​ m ℓ 2 (S) I 4 ​ (4) 3 5 ​ m ℓ 2

TestHub · Accepted Answer

For central horizontal axis 1, two rods are at distance ℓ/2; two rotate about their centres.

$I_{1} = 2 m (ℓ /2)^{2} + 2 (m ℓ^{2} /12)$

$I_{1} = \frac{2}{3} m ℓ^{2}$

For bottom axis 2, one rod lies on the axis and the top rod lies ℓ away.

$I_{2} = m ℓ^{2} + 2 (m ℓ^{2} /3)$

$I_{2} = \frac{5}{3} m ℓ^{2}$

Symmetry gives central vertical axis 4 and diagonal axis 3 the same moment as axis 1.

$I_{3} = I_{4} = \frac{2}{3} m ℓ^{2}$

P → 2; Q → 4; R → 2; S → 2. Option A.

List - I	List - II
(P) $I_{1}$	(1) $\frac{4}{3} m ℓ^{2}$
(Q) $I_{2}$	(2) $\frac{2}{3} m ℓ^{2}$
(R) $I_{3}$	(3) $\frac{1}{2} m ℓ^{2}$
(S) $I_{4}$	(4) $\frac{5}{3} m ℓ^{2}$

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