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 ?