Consider a thin uniform rod of mass M and length L, positioned along the z-axis with...

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Question

Consider a thin uniform rod of mass M and length L

Answer 1

Answer #1

a) consider an element of length dz and mass dm at a distance of z from mass m on the rod. Force due to this element will be Gmdm/z2. dm = Mdz/L.

Now for total mass integrate it from x = z to x = z+L.

F = GMm/z(z+L). Towards - z direction.

b). Consider an element of length dz at a distance of z from the upper end of lower rod having mass dm.

F on that dm will be GMdm/z(z+L).

DM will be again Mdz/L.

Now integrate it from z= L to z= 2L.

Answer 2

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