Three point masses are at the corners of an equilateral traingle of side `r`. Their separations do not change when the system rotates about the centre of the triangle. For this, the time period of rotation must be proportional to

Options

A. (i),(ii)
B. (ii),(iii)
C. (i),(iii)
D. (i),(iv)

Answer

D

Explanation

`F=(Gm^(2))/(a^(2)), r=a/(sqrt(3))`
Resultant force on `m=sqrt(3) F`
`sqrt(3)F=m omega^(2)r`
`sqrt(3)(Gm^(2))/(a^(2))=m omega^(2)a/(sqrt(3))`
`omega=sqrt((3Gm)/(a^(3)))`
`T=(2pi)/(omega)=(2pia^(3//2))/(sqrt(3Gm)), T prop a^(3//2), T propm^(-1//2)`