Four particles each of mass .m. are located at the four corners of a square of side a. If the system is revolving in a circle due to their mutual force of attractions then the angular velocity and time period of each particle is

Four particles each of mass .m. are located at the four corners of a s

1.	Four particles each of mass .m. are located at the four corners of a square of side a. If the system is revolving in a circle due to their mutual force of attractions then the angular velocity and time period of each particle is
Answer» Solution : From the FIG. `r=a//SQRT2` The resultant GRAVITATIONAL force on ONE of the particles `F_R=sqrt2(Gm^2)/a^2 + (Gm^2)/(2a^2)` This gravitational force provides the NECESSARY centripetal force `mromega^2 =(Gm)/a^2(sqrt2+1/2) rArr` `a/sqrt2 omega^2 =(Gm)/a^2((2sqrt2+1)/2) rArr omega=sqrt((Gm)/a^3(2+1/sqrt2))` `T=(2pi)/omega =2pi sqrt(a^3/(Gm)(sqrt2/(2sqrt2+1)))`