Infinite number of bodies each of mass 2 kg

Infinite number of bodies, each of mass $2\\,kg$ , are situated on x-axis at distances$1\\,m$ , $2\\,m$ , $4\\,m$ , $8\\,m$ ,……..respectively, from the origin. The resulting gravitational potential due to this system at the origin will beA. $ - G$B. $ - \\dfracG$D. $ - 4G$ Hint:Gravitational potential is defined as the amount of work done to move a given object from the reference point to a given point. Here, there are an infinite number of bodies, therefore, the gravitational potential will be calculated infinite times. Therefore, we will add the gravitational potentials of different potentials upto infinity. FORMULA USED: The formula of gravitational potential is given by $V = \dfrac$ $ \Rightarrow \,V = - 4G$ Therefore, gravitational potential due to the infinite number of bodies at the origin is $ - 4G$ . Hence, option (D) is the correct option. NOTE: Here, gravitational potential is always taken as negative because the work done to bring an object to infinity is done by gravitational pull and not the gravitational potential. Therefore, the answer is also negative. Here, we want to bring an infinite number of bodies to the origin, that is why we have added all the gravitational potentials.