Question

Three rods of mass M and length L constitutes in equilateral triangle find moment of inertia about an Axis passes through one corner and perpendicular to the base

Answer 1

$\Large\underline{\underline{\sf \blue{Given}:}}$

• Mass of rod = M

• Length of rod = L

$\Large\underline{\underline{\sf \blue{To\:Find}:}}$

• Moment of inertia about an Axis passes through one corner and perpendicular to the base = ?

$\Large\underline{\underline{\sf \blue{Solution}:}}$

Moment of Inertia of single rod about and axis passes through its centre and perpendicular to its :

$\implies{\sf \dfrac{1}{12}ML^2 }$

Moment of Inertia of each side of traingle about an Axis passing through the traingle's centre and perpendicular to its plane is

$\implies{\sf \dfrac{1}{12}ML^2+M\left(\dfrac{L}{2\sqrt{3}}\right)^2 }$

$\implies{\sf \dfrac{1}{6}ML^2}$

Moment of Inertia of traingle about this axis is :

$\implies{\sf 3×\dfrac{1}{6}ML^2}$

$\implies{\sf \dfrac{1}{2}ML^2}$

$\Large\underline{\underline{\sf \blue{Answer}:}}$

•°• Moment of inertia about an Axis passes through one corner and perpendicular to the base is $\bf{\frac{1}{2}ML^2}$