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Grade: 12

                        

A mass m is at a distance a from one end of a uniform rod of length l and mass M. The gravitational force on the mass due to the rod is ------------

9 years ago

Answers : (2)

vikas askiitian expert
509 Points
							

force on mass m due to rod is equal to force on rod due to mass so   (action equals to reaction)

 i am calculating force on rod due to mass...

let rod is placed in x axis  such that its one end is at a distance x from origin ...mass m is placed at origin...

consider a element dx on rod at a distance x from origin...

mass of this element = dm = (M/L)dx

force on this element due to rod is dF = Gmdm/x2

           dF = Gm(M/L)dx/x2

 integrating both sides

       [F] lim0 to F = -GMm/L (1/x)          lim x to x+L

      F = GMm/x(x+L) 

approve if u like it

9 years ago
Rishi Sharma
askIITians Faculty
614 Points
							Dear Student,
Please find below the solution to your problem.

force on mass m due to rod is equal to force on rod due to mass so (action equals to reaction)
i am calculating force on rod due to mass...
let rod is placed in x axis such that its one end is at a distance x from origin ...mass m is placed at origin...
consider a element dx on rod at a distance x from origin...
mass of this element = dm = (M/L)dx
force on this element due to rod is dF = Gmdm/x2
dF = Gm(M/L)dx/x2
integrating both sides
[F] lim0 to F = -GMm/L (1/x) lim x to x+L
F = GMm/x(x+L)

Thanks and Regards
3 months ago
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