Question

In the HCl molecule, the separation between the nuclei of the two atoms is about $1.27 \AA$ ($1 \AA=10^{-10} m$). Find the approximate location of the CM of the molecule given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

Answer 1

Let hydrogen ride is placed in Cartesian co-ordinate system in such a way that , hydrogen is located at origin and chlorine is located along x axis at 1.27A distance from the origin.

From definition of centre of mass.

Centre of mass , X = (m1x1+m2x2)/(m1+m2) 


Xcm = [mH(0) + mCl(1.27)]/(mH + mCl)


= mCl(1.27)/(mH + mCl)


= 35.5mH (1.27)/(mH + 35.5mH )


= 35.5x1.27/36.5


= 1.235 A


Hence the centre of mass is 1.235 A from the hydrogen atom along the line joining the two atom

Answer 2

Explanation:

diameter of sphere , d = 2a

so, radius of sphere , r = a

moment of inertia of sphere about an axis passing through its centre , I = 2/5ma² [ as sphere is solid ]

Moment of inertia of sphere which is located b distance from observations points , I' = mb² [ here we assume size of sphere is negligible compare of b ]