JEE Main · 2007 · 29 Apr 2007 · Offline · Rotational Mechanics

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For the given uniform square lamina ABCD, whose centre is O, which of the following is true? (E and F are the midpoints of AB and DC respectively.)

(A) $2 I_{A C} = I_{E F}$
(B) $I_{A D} = 3 I_{E F}$
(C) $I_{A C} = I_{E F}$ ✓ Correct
(D) $I_{A C} = 2 I_{E F}$

Answer: (C)

Solution

By the perpendicular-axis theorem for a plane lamina, the moment of inertia about an axis perpendicular to the plate through its centre equals the sum of the moments about any two perpendicular in-plane axes through that centre. The diagonal axis

A C

and the midline axis

E F

are just such a perpendicular pair of in-plane axes, and the fourfold symmetry of the square makes the lamina look identical about either one. Their moments of inertia are therefore equal, so

I_{A C} = I_{E F}

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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JEE Main · 2007 · 29 Apr 2007 · Offline · Rotational Mechanics

Solution

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