Two particles each of mass m, and other particle of mass 2 m are situated at the vertices of an equilateral triangle ABC of side L. What is the moment of inertia of the system about the line XY perpendicular to AB in the plane of ABC ?

Question

Two particles each of mass m, and other particle of mass 2 m are situated at the vertices of an equilateral triangle ABC of side L. What is the moment of inertia of the system about the line XY perpendicular to AB in the plane of ABC ? <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/f227383b5b01c53aa79ea7347ca61197-.png" /> (A) (3/2) mL 2 (B) 2 mL 2 (C) (5/4) mL 2 (D) Moment of Inertia of the system

Tardigrade Admin · Accepted Answer

Moment of inertia of the system I =IA+IB+IC=0+m L2+2 m ×((L/2))2 =m L2+(2 m L2/4) =m L2+(m L2/2) =(3/2) m L2

Q. Two particles each of mass $m$ , and other particle of mass $2 m$ are situated at the vertices of an equilateral triangle ABC of side $L$ . What is the moment of inertia of the system about the line XY perpendicular to $A B$ in the plane of $A BC$ ?

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

$2 m L^{2}$

$\frac{5}{4} m L^{2}$

Moment of Inertia of the system

Moment of inertia of the system
$I = I_{A} + I_{B} + I_{C} = 0 + m L^{2} + 2 m \times (\frac{L}{2})^{2}$
$= m L^{2} + \frac{2 m L ^{2}}{4}$
$= m L^{2} + \frac{m L ^{2}}{2}$
$= \frac{3}{2} m L^{2}$

Q. Two particles each of mass m, and other particle of mass 2m are situated at the vertices of an equilateral triangle ABC of side L. What is the moment of inertia of the system about the line XY perpendicular to AB in the plane of ABC ?

23​mL2

2mL2

45​mL2