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calculating gravitational force ,Fg on b/n 2 extended objects.
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m mass M,length L
while calculating Fg b/n m and M can we assume mass of rod to be concentrated at its centre of gravity . Xcog= integral(g(x)*dx))/integral(g(x)*dx)
Hii Shubam
Let the separation of the mass m from rod is r
Let a small mass on the rod of length dx from the body (m) at a distance x.
Then x can varry from r to r + L
Now mass of this small body is M.dx/L
Now gravitation force = GM1.M2/r^2
so G . m . M.dx /L(x)^2
Now we have to integrate it from r to r+L
F = GmM/L [ -1/x] from (r to r+L)
F = GmM / L [ -1/r+L + 1/r ] = GmM/L [ L/(r)(r+L) ] = GmM/r(r+L) ans
I hope ur question is solved now
With regards
Yagya
askiitians_expert
my question was'' can we assume mass to be concentrated at COG'' and if not why ?
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