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NEET
Exam
NEET
Subject
Physics
Chapter
Rotational Motion

NEET · Physics · Rotational Motion

Four rods of equal length l and mass m each from a square as shown...

Four rods of equal length ll and mass mm each from a square as shown in figure. Moment of inertia about three axes 1,2 and 3 are say I1,I2I_1, I_2 and I3I_3. Then, match the following columns (
Column IColumn II
(A)A_1(P)\tfrac{4}{3} m^2
(B)I_2(q)\tfrac{2}{3} m v^2
(C)I_3(r)\tfrac{1}{2} m m^2
(s)None of the above
)

Options

  1. Aa-r b-s c-p
  2. Ba-s b-r c-p
  3. Ca-q b-s c-p
  4. Da-q b-p c-s

Correct answer

C. a-q b-s c-p

Step-by-step solution

I1=2(ml22)+2(m)(l2)2=23ml2I2=0+2(ml23)+ml2=(53)ml2I3=4[ml23sin⁡245s]=23ml2=I1\begin{aligned} & I_1=2\left(\frac{m l^2}{2}\right) +2(m)\left(\frac{l}{2}\right)^2=\frac{2}{3} m l^2 \\ & I_2=0+2\left(\frac{m l^2}{3}\right)+m l^2=\left(\frac{5}{3}\right) m l^2 \\ & I_3=4\left[\frac{m l^2}{3} \sin ^2 45^{\mathrm{s}}\right]=\frac{2}{3} m l^2=I_1 \end{aligned})$
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