A diatomic molecule consists of two point masses, m1 and m2, separated by a distance r.If x is the distance from m1 to the centre of mass, find the moment of inertia in terms of x about an axis perpendicular to the molecular axis through the centre of mass.
A)0
B)m1m2 r2/m1 + m2
C)m1(r - x)2 + m2x2
D)m1x2 + m2(r - x)2
E)m2x2 + m1r2

Question

Quizplus · Accepted Answer

The moment of inertia of a diatomic molecule about an axis perpendicular to the molecular axis through the centre of mass is given by:

I = m1x2 + m2(r - x)2

where r is the distance between the two masses.

From the definition of the centre of mass, we have:

m1 x + m2 (r - x) = 0

Solving for x, we get:

x = m2r / (m1 + m2)

Substituting this value of x in the equation for I, we get:

I = m1 (m2r / (m1 + m2))2 + m2 (r - m2r / (m1 + m2))2

Simplifying, we get:

I = m1m2r2 / (m1 + m2) + m2(m1r2) / (m1 + m2)2

I = m1m2r2 / (m1 + m2)2 + m1r2 / (m1 + m2)

I = (m1r2 + m2(m1 + m2 - r)x2) / (m1 + m2)

I = m1x2 + m2(r - x)2

Therefore, the moment of inertia is given by D) m1 x2 + m2(r - x)2.

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