First slide

Moment of intertia

Question

Four rods of equal length I and each of mass m form a square as shown in figure.
Moments of inertia about three axes 1, 2 and 3 are say I₁,I₂ and I₃• Then, match the following columns
and mark the correct option from the codes given below.
Column I
(A)   I₁
(B)   I₂
(C) I₃
Column II
(p)    $\frac{4}{3} m l^{2}$
(q)    $\frac{2}{3} m l^{2}$
(r ) $\frac{1}{2} m l^{2}$
(s) None

Moderate

A

A B C
q s p
B

A B C
p s q
C

A B C
r p q
D

A B C
q s q

Solution

$( A) I_{1} = 2 (\frac{m l^{2}}{12}) + 2 (m) {(\frac{l}{2})}^{2} = \frac{2}{3} m l^{2}$
$(B) I_{2} = 0 + 2 (\frac{m l^{2}}{3}) + m l^{2} = (\frac{5}{3}) m l^{2}$
$(C) I_{3} = 4 [\frac{m l^{2}}{3} \sin^{2} 45 °] = \frac{2}{3} m l^{2} = I_{1}$
Hence, $A \to q, B \to s, C \to q$

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