Question

The distance between the centre of carbon and oxygen in CO molecule is 0.12 mm.the distance of centre of mass from the carbon atom is

Answer 1

Explanation:

Let m1 and m2 be the masses of carbon and oxygen atom respectively. Let 'd' be the distance of seperation between the centers of carbon and oxygen atoms.

Let x1 - be the position of the carbon

and x2 - be the position of the oxygen atom

begin mathsize 14px style We space can space write space the space centre space of space mass space of space this space system space as : straight x subscript cm equals fraction numerator straight m subscript 1 straight x subscript 1 plus straight m subscript 2 straight x subscript 2 over denominator straight m subscript 1 plus straight m subscript 2 end fraction minus minus minus minus minus minus minus minus minus minus minus minus left parenthesis 1 right parenthesis Here space we space need space to space find space the space position space of space the space centre space of space mass space of space CO space molecule space with space respect space to space carbon space atom so space straight x subscript 1 equals 0 space straight m space and space straight x subscript 2 space equals 1.130 cross times 10 to the power of minus 10 end exponent straight m straight m subscript 1 minus mass space of space carbon space atom space equals space 12 space straight U space and space straight m subscript 2 minus mass space of space oxygen space atom space equals space 16 space straight U On space substituting space in space left parenthesis 1 right parenthesis space we space get : straight x subscript cm equals fraction numerator open parentheses 12 cross times 0 close parentheses plus open parentheses 16 cross times 1.130 cross times 10 to the power of minus 10 end exponent close parentheses over denominator 12 plus 16 end fraction space space space space space equals 6.46 space cross times 10 to the power of minus 11 end exponent space straight m straight x subscript cm equals 0.646 cross times 10 to the power of minus 10 end exponent straight m end style

Hence the position of centre of mass of CO molecule with respect to carbon atom = 0.646 × 10-10m.