Question

A double star is a system of two stars (say masses m1 and m2) moving around the centre of inertia of the sustem due to gravitation . Then , ratio of sweeps area of atar of mas m1 to the star of the mass m2is .............................

Ans given in book is : m2 2/m1 2

Answer 1

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

THANKS