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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 ------------

rajan jha , 15 Years ago

Grade 12

2 Answers

vikas askiitian expert

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

Approved

Last Activity: 15 Years ago

Rishi Sharma

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

Last Activity: 5 Years ago

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