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A particle of mass m is situated at a di...

A particle of mass `m` is situated at a distance `d` from one end of a rod of mass `M` and length `L` as shown in diagram. Find the magnitude of the gravitational force between them

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Let us consider an elementry mass dm of length dr at a distance r from the particle of mass m . Here `dm = M/L ` dr. The gravitational force dF on m due to this elementry mass dm is `dF = (Gm)/(r^(2)) dm = (GmM)/(Lr^(2)) `dr
` :. " " F = (GMm)/L int_(d)^(L+d)(dr.)/(r^(2)) = (GMm)/L [-1/r]_(d)^(L+d)`
` = (-GmM)/L [1/(L+d)-1/d] `
` =(GMm)/(d(L+d))`
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