1.

The magnitude of the gravitational potential at point O will be

Answer»

`(Gm)/(2r)`
`(Gm)/(r)`
`(3GM)/(2r)`
`(2GM)/(r)`

Solution :The gravitational potential at POINT O, in magnitude is
`V=Gm[(1)/(r)+(1)/(2r)+(1)/(4r)+(1)/(8R)+…]`
`=(Gm)/(r)[1+(1)/(2)+(1)/(4)+(1)/(8)+…]`
`=(Gm)/(r)[(1)/(2^(0))+(1)/(2^(1))+(1)/(2^(2))+(1)/(2^(3))+…]`
`=(Gm)/(r)((1)/(1-(1)/(2)))=(2Gm)/(r)`


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