JEE Advanced 2026 · Paper 1 · Physics Q16

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PhysicsList match+4 / -1Question 32 of 48

List-I shows four planar structures made of uniform solid rods each of mass $m$ and length $l$ . In the List-II the possible moment of inertia of these structures about an axis $OCO'$ , which lies in the plane of the structures, are given.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

List-I

List-II

1
$\frac54ml^2$
2
$\frac16ml^2$
3
$\frac1{12}ml^2$
4
$\frac23ml^2$
5
$\frac13ml^2$

P→ 5, Q→ 1, R→ 4, S→ 2

P→ 1, Q→ 3, R→ 4, S→ 2

P→ 5, Q→ 3, R→ 2, S→ 1

P→ 5, Q→ 4, R→ 2, S→ 1

Answer and worked solution

Official answer: A

A rod of length $l$ with one end on the axis, at angle $\phi$ to it, has $I=\frac13ml^2\sin^2\phi$ .

(P) Two rods at $45^\circ$ : $2\cdot\frac13ml^2\cdot\frac12=\frac13ml^2$ → 5.

(Q) $CA$ and $CB$ at $60^\circ$ and $120^\circ$ to the axis: $\frac14ml^2$ each. $AB$ is parallel to the axis at distance $l\sin60^\circ$ : $\frac34ml^2$ . Total $\frac54ml^2$ → 1.

(R) About the diagonal $AC$ , each of the four sides is at $45^\circ$ with one end on the axis: $4\cdot\frac16ml^2=\frac23ml^2$ → 4.

(S) Two rods at $30^\circ$ : $2\cdot\frac13ml^2\cdot\frac14=\frac16ml^2$ → 2.

P→5, Q→1, R→4, S→2.

Topics:Moment of inertia Parallel and perpendicular axis theorems

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