Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period will be

Question

Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period will be (A) 4 π √(a3/ G m) (B) 2 π √(4 √3 a3/ Gm (5 √3+4)) (C) 4 π √(3 a3/ G m) (D) None of these

Tardigrade Admin · Accepted Answer

Correct answer is (b) 2 π √(4 √3 a3/ Gm (5 √3+4))

Q. Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length $a$ . Their common time period will be

$4 π \frac{a ^{3}}{G m}$

$2 π \frac{4 3 a ^{3}}{G m ( 5 3 + 4 )}$

$4 π \frac{3 a ^{3}}{G m}$

None of these

Correct answer is (b) $2 π \frac{4 3 a ^{3}}{G m ( 5 3 + 4 )}$

Q. Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period will be

4πGma3​​

2πGm(53​+4)43​a3​​

4πGm3a3​​