(a) Consider an element dx at a distance x from the load (x = 0). If T (x) and T (x + dx) are tensions on the two cross sections a distance dx apart, then
T (x +dx) – T(x) = μgdx (where μ is the mass/length)
(dT/dx)dx = μgdx
⇒T(x) = μgx +C
At x = 0, T(O) = Mg ⇒ C ⇒ Mg
T(x) = μgx + Mg
Let the length dx at x increase by dr, then
(m is the mass of the wire)