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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)


 

6 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

6 years ago
shubham tomar
31 Points
										

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

6 years ago
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