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Q.

Infinite number of masses, each of mass m,  are placed along a straight line at distance of r,2r,4r,8r, etc. from a reference point O .The magnitude of the gravitational potential at point O  will be

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a

Gm2r

b

Gmr

c

3Gm2r

d

2Gmr

answer is D.

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Detailed Solution

The gravitational potential, in magnitude, at point O  is   V=Gm[1r+12r+14r+18r+....]       =Gmr[1+12+14+18+....]      =Gmr[120+121+122+123+....]      =Gmr(11−12)=2Gmr
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