Four identical rods are joined end to end to form a square. The mass of each rod is M. The moment of inertia of the square about the median line is

Question

Four identical rods are joined end to end to form a square. The mass of each rod is M. The moment of inertia of the square about the median line is (A) (M l2/3) (B) (M l2/4) (C) (M l2/6) (D) (2 M l2/3)

Tardigrade Admin · Accepted Answer

I text median line =IA+IB+IC+ID =2 × (M l2/12)+2 M((l/2))2 =(M l2/6)+(M l2/2)=(2/3) M l2

Q. Four identical rods are joined end to end to form a square. The mass of each rod is $M$ . The moment of inertia of the square about the median line is

$\frac{M l ^{2}}{3}$

$\frac{M l ^{2}}{4}$

$\frac{M l ^{2}}{6}$

$\frac{2 M l ^{2}}{3}$

$I_{median line} = I_{A} + I_{B} + I_{C} + I_{D}$
$= 2 \times \frac{M l ^{2}}{12} + 2 M (\frac{l}{2})^{2}$
$= \frac{M l ^{2}}{6} + \frac{M l ^{2}}{2} = \frac{2}{3} M l^{2}$

Q. Four identical rods are joined end to end to form a square. The mass of each rod is M. The moment of inertia of the square about the median line is

3Ml2​

4Ml2​

6Ml2​

32Ml2​