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Find the potential energy of the gravita...

Find the potential energy of the gravitational interation of a point mass of mass m and a thin uniform rod of mass `M` and length l, if they are located along a straight line such that the point mass is at a distance 'a' from one end. Also find the force of their interaction.

Text Solution

Verified by Experts

The correct Answer is:
`-(GMm)/(l)log_(e)(1+(l)/(a))`

`U=(GM_(1)M_(2))/(d)` for the point mass
`dU=(GmdM)/(x)impliesU=-int(GMm)/(lx)dx`
`U=-(GMm)/(l)int_(a)^(l+a)(dx)/(x)=-(GMm)/(l)ln((l+a)/(a))`
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