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)

shubham tomar Grade: 12

        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)

7 years ago

Answers : (2)

Askiitians_Expert Yagyadutt

askIITians Faculty

74 Points

										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