3 point masses each of mass m are at corners of an equilateral triangle of side r their separation do not change when the system rotates about the center of the triangle

 

For this the time period of rotation is proportional to

 

a] r

 

b] r^1.5

 

c) m

 

d) m^-0.5

 

Please give detailed soution rates assured

ans is d

take any point mass let say a

b and c will exert gravitational force on a . they will be = in magnitude= f

let the angle bw the 2 forces on a be  .than the resultant of both the f's is

3f...

similarly for b and c also the resultant gravitational force is 3f.inclined at angle 30 to each side

now all these forces meet at the centre of the triangle. now the the radius of rotation is R =r/ 3

so we get

mv²3/r = Gm3/r²

so v =Gm/r

 

rate if useful