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)

Question

calculating gravitational force ,Fg on b/n 2 extended objects.

0 ---------------------------------------------

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)

Askiitians_Expert Yagyadutt · Answer

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

shubham tomar · Answer

my question was'' can we assume mass to be concentrated at COG'' and if not why ?

2 Answers