A square frame ABCD is formed by four identical rods each of mass 'm' and length 'T'. This frame is in X - Y plane such that side AB coincides with X - axis and side AD along Y - axis. The moment of inertia of the frame about X - axis is

Home » A square frame ABCD is formed by four identical rods each of mass ‘m’ and length ‘T’. This frame is in X – Y plane such that side AB coincides with X – axis and side AD along Y – axis. The moment of inertia of the frame about X – axis is

A square frame ABCD is formed by four identical rods each of mass ‘m’ and length ‘T’. This frame is in X – Y plane such that side AB coincides with X – axis and side AD along Y – axis. The moment of inertia of the frame about X – axis is

Physics | Physics

A square frame ABCD is formed by four identical rods each of mass ‘m’ and length ‘T’. This frame is in X – Y plane such that side AB coincides with X – axis and side AD along Y – axis. The moment of inertia of the frame about X – axis is

2ml²/3
4ml²/3
5ml²/3
ml²/12

Solution: The correct answer is

The inertia moments of rods AD and BC are as follows: $\frac{1}{3}m{{T}^{2}}$

Because rod AB is on the X-axis, its moment of inertia is zero, and so r=0.
Because every element in rod CD is at a distance T from the X-axis, its moment of inertia is as follows: $m{{T}^{2}}$ .

Hence, $I=2\times \frac{1}{3}m{{T}^{2}}\times m{{T}^{2}}$

=> $I=\frac{5}{3}m{{T}^{2}}$

i

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