A particle of mass m is placed at a distance d from one end of a uniform rod with length L and mass M as shown in the figure . Find the magnitude of the gravitational firce on the particle due to the rod
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magnitude of gravitational force on the particle due to rod is GM²/d(L + d)
mass of rod is M,
an elementary length of dx is cut x distance from the point mass m .
so, mass of element, dm = M/L dx
now force acting on mass m, dF =
Gm.dm/x²
= GM(M/L dx)/x²
=GM²/L ∫ (1/x²)dx
= GM²/L [-1/x]^(L+d)_d
= -GM²/L [1/(L + d) - 1/d]
= -GM²/L [ -L/d(L + d) ]
= GM²/d(L + d)
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