A triatomic molecule is oriented as follows along the x -axis: mass m is at the origin, mass 2 m is at x=a , and, mass 3 m is at x=2 a . What is the moment of inertia of this molecule about the y -axis?
A) $3 m a ^ { 2 }$
B) $14 m a ^ { 2 }$
C) $2 m a ^ { 2 }$
D) $12 m a ^ { 2 }$

Question

A triatomic molecule is oriented as follows along the  x -axis: mass  m  is at the origin, mass  2 m  is at  x=a , and, mass  3 m  is at  x=2 a . What is the moment of inertia of this molecule about the  y -axis?
A) $3 m a ^ { 2 }$
B) $14 m a ^ { 2 }$
C) $2 m a ^ { 2 }$
D) $12 m a ^ { 2 }$

Quizplus · Accepted Answer

The moment of inertia $I$ about the y-axis for a system of particles is given by $I = \sum m_i r_i^2$, where $m_i$ is the mass of the i-th particle and $r_i$ is the distance of the i-th particle from the axis of rotation. For the given molecule, the moment of inertia about the y-axis is calculated as follows: $I = m(0)^2 + 2m(a)^2 + 3m(2a)^2 = 0 + 2ma^2 + 12ma^2 = 14ma^2$.

A Triatomic Molecule Is Oriented as Follows Along the 3ma23 m a ^ { 2 }3ma2

A Triatomic Molecule Is Oriented as Follows Along the $3 m a ^ { 2 }$