An infinite number of particles each of mass m are placed on the positive x-aris at lm, 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-aris at lm, 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><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_NEO_CAO_PHY_XI_V01_MP2_C09_SLV_018_S01.png" width="80%"/> <br/> The resultant gravitational force <br/> `F = (Gm^2)/1+(Gm^2)/<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>+(Gm^2)/16 +........`<br/> `=Gm^(2)(1/1+1/4+1/16+ .........)= Gm^(2)(1/(1-(1)/4))` <br/> ( `:. ` <a href="https://interviewquestions.tuteehub.com/tag/sum-1234400" style="font-weight:bold;" target="_blank" title="Click to know more about SUM">SUM</a> of the <a href="https://interviewquestions.tuteehub.com/tag/infinite-515764" style="font-weight:bold;" target="_blank" title="Click to know more about INFINITE">INFINITE</a> terms in G.P is `S_(prop) = a/(1-r))=4/3Gm^2`</body></html>