Question

A thin rod of length 'L' and mass ‘M’ is bent at the middle point O at an angle of 60°. The moment of inertia of the rod about an axis passing through point 'O' and perpendicular to the plane of the rod will be ______.

विकल्प

• \[\frac{\mathrm{ML}^2}{6}\]

• \[\frac{\mathrm{ML}^2}{12}\]

• \[\frac{\mathrm{ML}^2}{24}\]

• \[\frac{\mathrm{ML}^2}{3}\]

Answer 1

A thin rod of length 'L' and mass ‘M’ is bent at the middle point O at an angle of 60°. The moment of inertia of the rod about an axis passing through point 'O' and perpendicular to the plane of the rod will be \[\frac{\mathrm{ML}^2}{12}\].

Explanation:

Moment of inertia of rod about an axis passing through one end is given by, \[\mathrm{I}=\frac{\mathrm{ML}^2}{3}\]

\[\therefore\] Moment of inertia of each half of the rod about the midpoint is given by,

\[\mathrm{I}=\frac{\frac{M}{2}\left(\frac{L}{2}\right)^{2}}{3}=\frac{\mathrm{ML}^{2}}{24}\]

Total moment of inertia \[=\mathrm{I}=2\mathrm{I}_{1}=\frac{\mathrm{ML}^{2}}{12}\]