A very large number of particles of same mass m are kept at horizontal distances of 1m, 2m, 4m, 8mand so on from (0, 0) point The total gravitational potential at this point (0, 0) is(A)- 8G m8-3.(B)-3G m(C)-4G m(D)- 2G m

A very large number of particles of same mass m are kept at horizontal

1.	A very large number of particles of same mass m are kept at horizontal distances of 1m, 2m, 4m, 8mand so on from (0, 0) point The total gravitational potential at this point (0, 0) is(A)- 8G m8-3.(B)-3G m(C)-4G m(D)- 2G m
Answer» <p>Gravitational potential at pointris given by,</p><p>V = - Gm/r</p><p>According to the problem the gravitational potential by infinite masses at the origin is,</p><p>V = -Gm (1 + 1/2 + 1/4 + 1/8+...)</p><p>This is a geometric series with ratio 1/2</p><p>So,</p><p>V = -Gm2. As(sum of infinite terms of G.P. = 1/(1-1/2 ) = 2</p><p>= - 2Gm</p>