Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then :

Question

Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then : (A) I > (ma2/12) (B) (ma2/24) < I < (ma2/12) (C)  I = (ma2/12) (D)  I = (ma2/24)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ab6ede7b95f04b734e1b7fd43e81de8b-.png" /> Iz=(m a2/6) Using perpendicular axis theorem 2 Id=Iz ⇒ Id=(m a2/12)

Q. Consider a thin uniform square sheet made of a rigid material. If its side is ' $a$ ', mass $m$ and moment of inertia $I$ about one of its diagonals, then :

$I > \frac{m a ^{2}}{12}$

$\frac{m a ^{2}}{24} < I < \frac{m a ^{2}}{12}$

$I = \frac{m a ^{2}}{12}$

$I = \frac{m a ^{2}}{24}$

$I_{z} = \frac{m a ^{2}}{6}$ Using perpendicular axis theorem
$2 I_{d} = I_{z} \Rightarrow I_{d} = \frac{m a ^{2}}{12}$

Q. Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then :

I>12ma2​

24ma2​<I<12ma2​

I=12ma2​

I=24ma2​