(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)