An infinite number of particles each of mass m are placed on the positive x-axis at 1m, 2m, 4m, 8m,…. from the origin. The magnitude of the resultant gravitational force on mass 'm' kept at the origin is

An infinite number of particles each of mass m are placed on the posit

1.	An infinite number of particles each of mass m are placed on the positive x-axis at 1m, 2m, 4m, 8m,…. from the origin. The magnitude of the resultant gravitational force on mass 'm' kept at the origin is
Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C09_SLV_015_S01.png" width="80%"/> <br/> The resultant gravitational <a href="https://interviewquestions.tuteehub.com/tag/force-22342" style="font-weight:bold;" target="_blank" title="Click to know more about FORCE">FORCE</a> <br/> `F = (Gm^(2))/(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) + (Gm^(2))/(4) + (Gm^(2))/(16)+…..` <br/> `= Gm^(2)((1)/(1)+(1)/(4)+(1)/(16)+….) = Gm^(2)((1)/(1-(1)/(4)))` <br/> (`because` sum of the <a href="https://interviewquestions.tuteehub.com/tag/infinit-2737095" style="font-weight:bold;" target="_blank" title="Click to know more about INFINIT">INFINIT</a> <a href="https://interviewquestions.tuteehub.com/tag/trms-3834233" style="font-weight:bold;" target="_blank" title="Click to know more about TRMS">TRMS</a> in G.P is `S_(prop) = (a)/(1-r)`) <br/> `= (4)/(3)Gm^(2)`</body></html>