A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r.Find the moment of inertia through the centre of mass about an axis perpendicular to the molecular axis.
A)m1m2r2/(m1 + m2)
B)[(m1m2/m1) + m2]r2
C)(m1 + m2)/m1m2r2
D)(m1 + m1)r2 /m1m2
E)m1m2r2/m1

Question

Quizplus · Accepted Answer

The moment of inertia of a diatomic molecule about an axis perpendicular to the molecular axis can be calculated as follows:
I = m1r1^2 + m2r2^2
where r1 and r2 are the distances of the two masses from the axis of rotation which passes through the centre of mass.
Since the molecule is diatomic, the centre of mass is located at the midpoint between the two masses, i.e., r1 = r2 = r/2, where r is the distance between the two masses.
Therefore, I = m1(r/2)^2 + m2(r/2)^2
I = m1m2r^2/(m1 + m2)
Hence, the correct choice is (A).

A Diatomic Molecule Consists of Two Point Masses, M1 and M2