Three rods each of mass m and length L are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

Question

Three rods each of mass m and length L are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane? (A) 2 mL 2 (B) (m L2/2) (C) (m L2/3) (D) (m L2/6)

Tardigrade Admin · Accepted Answer

Using parallel axis theorem for one rod I=(m l2/12)+m((l/2 √3))2 For all three rods I' =3I =3 ml2[(1/12)+(1/12)] =(m l2/2)

Q. Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

$2 m L^{2}$

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

$\frac{m L ^{2}}{3}$

$\frac{m L ^{2}}{6}$

Using parallel axis theorem for one rod
$I = \frac{m l ^{2}}{12} + m (\frac{l}{2 3})^{2}$
For all three rods
$I^{'} = 3 I$
$= 3 m l^{2} [\frac{1}{12} + \frac{1}{12}]$
$= \frac{m l ^{2}}{2}$

Q. Three rods each of mass m and length L are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

2mL2

2mL2​

3mL2​

6mL2​