A uniform thin bar of mass 6 m and length 12 L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is:

Question

A uniform thin bar of mass 6 m and length 12 L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is: (A) 20 mL 2 (B) 6 m L2 (C) (12/5) m L2 (D) 30 mL 2

Tardigrade Admin · Accepted Answer

x=2 L cos 30°=L √3 I=6((m(2 L)2/12)+m x2)=20 m L2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/766984285d9d78b33822e1557d3dbc3c-.png" />

Q. A uniform thin bar of mass $6 m$ and length $12 L$ is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is:

$20 m L^{2}$

$6 m L^{2}$

$\frac{12}{5} m L^{2}$

$30 m L^{2}$

$x = 2 L cos 3 0^{\circ} = L 3$
$I = 6 (\frac{m ( 2 L ) ^{2}}{12} + m x^{2}) = 20 m L^{2}$

Q. A uniform thin bar of mass 6m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is:

20mL2

6mL2

512​mL2

30mL2