A ''double star'' is a composite system of two stars rotating about their center of mass under their mutual gravitational attraction. Let us consider such a ''double star'' which has two stars of masses 'm' and '2m' at a separation '1'. If T is the time period of rotation about their enter of mass then.

Question

A ''double star'' is a composite system of two stars rotating about their center of mass under their mutual gravitational attraction. Let us consider such a ''double star'' which has two stars of masses 'm' and '2m' at a separation '1'. If T is the time period of rotation about their enter of mass then. (A) T=2π√(l3/mG) (B) T=2π√(l3/2mG) (C) T=2π√(l3/3mG) (D) T=2π√(l3/4mG)

Tardigrade Admin · Accepted Answer

consider origin at pratical of mass 2m, we have centre of mass is 1/3 and 21/3 from m. (2l/3) ω2 = (Gm(2m)/l2) then find T

$T = 2 π \frac{l ^{3}}{m G}$

$T = 2 π \frac{l ^{3}}{2 m G}$

$T = 2 π \frac{l ^{3}}{3 m G}$

$T = 2 π \frac{l ^{3}}{4 m G}$

consider origin at pratical of mass 2m, we have centre of mass is 1/3 and 21/3 from m. $\frac{2 l}{3} ω^{2} = \frac{G m ( 2 m )}{l ^{2}}$ then find T

T=2πmGl3​​

T=2π2mGl3​​

T=2π3mGl3​​

T=2π4mGl3​​

consider origin at pratical of mass 2m, we have centre of mass is 1/3 and 21/3 from m. 32l​ω2=l2Gm(2m)​ then find T

$T = 2 π \frac{l ^{3}}{m G}$

$T = 2 π \frac{l ^{3}}{2 m G}$

$T = 2 π \frac{l ^{3}}{3 m G}$

$T = 2 π \frac{l ^{3}}{4 m G}$

consider origin at pratical of mass 2m, we have centre of mass is 1/3 and 21/3 from m. $\frac{2 l}{3} ω^{2} = \frac{G m ( 2 m )}{l ^{2}}$ then find T