1)

 Four particles, each  of mass M and equidistant from each other,  move along  a circle of radius  R under the action  of their mutual  gravitational attraction, the speed of each particle


A) GMR

B) 22GMR

C) GMR(1+22)

D) 12GMR(22+1)

Answer:

Option D

Explanation:

Net force acting on anyone particle M,

1532021730_M10.JPG

=GM2(2R)2+GM2(R2)2cos450+GM2(R2)2cos450

              =GM2R2(14+12)

 this force will equal to centripetal force.

 So,    MV2R=GM2R2(14+12)

            v=GM4R(1+22)

                =12GMR(22+1)

 Hence, speed of each particle in a circular motion is 

           12GMR(22+1)