Question

NEET & AllMS
NEET &
27.
A homogeneous bar of length L and mass M is at
a distance h from a point mass ma shown. The
force on m is F, then find F

Answer 1

Explanation:

Consider a small element dx of the rod at a distance x from the left end of the rod.

Mass of this small element is dM = M/Ldx

Distance of this small element from mass m is x + h.

Force on m due to this small element is dF = GmdM/(x +h)^2

To get the total force F on the mass m we integrate dF from x= 0 to x = L

F = ∫^x=L and x = 0 GmM/L dx/ (x + h)^2 = - GMm/L (1/L + h - 1/L)

                         = GmMh/L(L +h)

Thus the force on m due to homogeneous bar is GMmh/L(L +h).

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