Question

Four thin rods of same mass M and same length l, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

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

Answer 1

Answer: (A)

$\frac { 4 } { 3 } M l ^ { 2 }$

Answer 2

Moment of inertia of rod AB about point $P = \frac { 1 } { 12 } M l ^ { 2 }$

M.I. of rod AB about point O $= \frac { M l ^ { 2 } } { 12 } + M \left( \frac { l } { 2 } \right) ^ { 2 }$ $= \frac { 1 } { 3 } M l ^ { 2 }$

[by the theorem of parallel axis]

and the system consists of 4 rods of similar type so by the symmetry $I _ { \text {System } } = \frac { 4 } { 3 } M l ^ { 2 }$ .