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here in the question ,we have two masses which are moving under the influence of their mutual gravitational force...
both of them are moving about their center of mass in a circular orbits of different radii..
if R1 & R2 are radius of lighter and heavior particle respectively then
R1 +R2 = R ................1
Fc =mW12 R1 ..................2 (gravitional force will provide necassery centripital force)
Fc=2mW22R2 .......................3
dividing 1 & 2
(W1/W2)2 =2(R2/R1) .............4
ratio of kinetic energy is (KE)2/(KE)1=2(W2/W1)2 (R2/R1)2
from eq 4 substituting (W2/W1)
ratio =2(R2/R1) ...................5
now we have R1=2mR/3m=2R/3 & R2=mR/3m=R/3
after substituting these we get
ratio = 1:1
see the eq 5 , the ratio instead of 2(R2/R1) ,it is (R2/R1),
now u will will get ratio as 1:2 not 1:1 ...
sometimes calculations mistake may be there in the sol ,so see the concept and do it urself ....
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