To find the extension of the rod, we can use the formula:
delta = PL / (AE)
where delta is the extension, P is the axial load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity.
The cross-sectional area of the rod varies along its length, so we need to find the average area. The average diameter is:
(5 + 3) / 2 = 4 cm
The average area is:
A = pi/4 x (4)^2 = 12.57 cm^2
Substituting the given values, we get:
delta = 6000 x 50 / (12.57 x 2 x 10^5) = 0.015 cm
Therefore, the extension of the rod is 0.015 cm.