Question

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

• A. $\frac { M l ^ { 2 } } { 6 }$
• B. $\frac { M l ^ { 2 } } { 12 }$
• C. $\frac { M l ^ { 2 } } { 3 }$
• D. $\frac { M l ^ { 2 } } { 4 }$

Answer 1

Answer: (B)

$\frac { M l ^ { 2 } } { 12 }$

Answer 2

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 $I _ { z } = I _ { B _ { 1 } } + I _ { B _ { 2 } }$ $= 2 I _ { B _ { 1 } } = 2 I _ { B _ { 2 } } = \frac { M l ^ { 2 } } { 6 }$ [As $I _ { B _ { 1 } } = I _ { B _ { 2 } }$]

∴ $I _ { B _ { 1 } } = I _ { B _ { 2 } } = \frac { M l ^ { 2 } } { 12 }$.