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Find F("net") = GMm[ (1)/(r^(2))+ (1)/(2...

Find `F_("net") = GMm[ (1)/(r^(2))+ (1)/(2r^(2))+ (1)/(4r^(2))+ ...... "up to "oo]`.

Text Solution

Verified by Experts

The correct Answer is:
`F_("net")= (2GMm)/(r^(2))`
`F_("net") = GMm[ (1)/(r^(2)) + (1)/(2r^(2))+ (1)/(4r^(2))+ .....oo]`
`= GMm [ (1//r^(2))/(1- (1)/(2))] = (2GMm)/(r^(2))`
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