Two identical rods each of mass 'M' and length 'l' are joined in crossed positio

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Two identical rods each of mass 'M' and length 'l' are joined in crossed position as shown in figure. The moment of inertia of this system about a bisector would be

Two Identical Rods Each Of Mass 'M' And Length 'l' Are Joine...

Options:

A . Ml26

B . Ml212

C . Ml23

D . Ml24

Answer: Option B
:
B
Moment of inertia of system about an axes which is perpendicular to plane of rods and passing through the common centre of rods

I_{z} = \frac{M l^{2}}{12} + \frac{M l^{2}}{12} = \frac{M l^{2}}{6}

Again from perpendicular axes theorem

I_{2} = I_{B_{1}} + I_{B_{2}} = 2 I_{B_{1}} = 2 I_{B_{2}} = \frac{M l^{2}}{6}

[As

I_{B_{1}} = I_{B_{2}}]

∴ I_{B_{1}} = I_{B_{2}} = \frac{M l^{2}}{12} .

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