Question

Three rods each of lenght L and mass M are placed along X, Y and Z axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this sytem about Z axis is:

• A. $\frac { 2 \mathrm { ML } ^ { 2 } } { 3 }$
• B. $\frac { 4 \mathrm { ML } ^ { 2 } } { 3 }$
• C. $\frac { 5 \mathrm { ML } ^ { 2 } } { 3 }$
• D. $\frac { \mathrm { ML } ^ { 2 } } { 3 }$

Answer 1

Answer: (A)

$\frac { 2 \mathrm { ML } ^ { 2 } } { 3 }$

Answer 2

M.I. of rod (1) about Z-axis I1

= $I _ { 1 } = \frac { M l ^ { 2 } } { 3 }$

M.I. of rod (2) about Z-axis I2=$I _ { 2 } = \frac { M l ^ { 2 } } { 3 }$

M.I. of rod (3) about Z-axis I3 = 0

Because this rod lies on Z-axis

$\therefore$