A double star system consists of two stars having masses M and 2M. The distance between their centers is r. They revolve under their mutual gravitational attraction. Then the incorrect options are____
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a
Heavier star revolve in an orbit of radius 2r3
b
Both stars revolve with the same period which is equal to 2π3r32GM1/2
c
Kinetic energy of heavy star is twice that of light star.
d
Angular momentum of both stars about common center of mass are not equal
answer is A.
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Detailed Solution
(i) they revolve about their C.O.M with same ‘ω’r1=2MM+2M r=2r3=radius of small star r2=MM+2M r=r3=radius of big star (iv) L1=M2r32ω L2=2Mr32ω ∴L1≠L2 (ii) M.2r3.ω2=G.M.2Mr2 ⇒ω2=2GMr2.2r3 ⇒ω2=3GMr3 ∴T=2πr33GM (iii) K.Esmall=12M2r32ω2=2Mr2ω29 K.Ebig=122Mr32ω2=Mr2ω29