Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

Question

Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The period of revolution is : (A) (1/2 π) √( d 3/3 Gm ) (B) 2 π √( d 3/3 Gm ) (C) (1/2 π) √(3 Gm / d 3) (D) 2 π √(3 Gm / d 3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c49a6b2bdcc3ad0d9ea4980cc5d90ce0-.png" /> F=(G(2 m) m/d2)=(2 m) ω2(d / 3) (G m/d2)=ω2 (d/3) ⇒ ω2=(3 G m/d3) ⇒ ω=√(3 G m/d3) ⇒ T=(2 π/ω)=2 π √(d3/3 G m)

Q. Two stars of masses $m$ and $2 m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is :

$\frac{1}{2 π} \frac{d ^{3}}{3 G m}$

$2 π \frac{d ^{3}}{3 G m}$

$\frac{1}{2 π} \frac{3 G m}{d ^{3}}$

$2 π \frac{3 G m}{d ^{3}}$

$F = \frac{G ( 2 m ) m}{d ^{2}} = (2 m) ω^{2} (d /3)$
$\frac{G m}{d ^{2}} = ω^{2} \frac{d}{3}$
$\Rightarrow ω^{2} = \frac{3 G m}{d ^{3}}$
$\Rightarrow ω = \frac{3 G m}{d ^{3}}$
$\Rightarrow T = \frac{2 π}{ω} = 2 π \frac{d ^{3}}{3 G m}$

Q. Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

2π1​3Gmd3​​

2π3Gmd3​​

2π1​d33Gm​​

2πd33Gm​​