A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100 °C to just below the eutectoid temperature (723 °C). A part of the iron-cementite phase diagram is shown in the figure. The ratio of the pro-eutectoid cementite content to the total cementite content in the microstructure that develops just below the eutectoid temperature is ________.

(Rounded off to two decimal places)

A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (p) in MPa for the above process is related to extrusion ratio (r) as

$\rm p=K_s σ_m\left[0.8+1.5\ ln(r)+\frac{2l}{d_0}\right] $

where σ_m, is the mean flow strength of the billet material in MPa, l is the portion of the billet length remaining to be extruded in mm, d₀ is the initial diameter of the billet in mm, and K_s is the die shape factor.

If the mean flow strength of the billet material is 50 MPa and the die shape factor is 1.05, then the maximum force required at the start of extrusion is _______ kN (round off to one decimal place).

A rod of length $$20$$ $$mm$$ is stretched to make a rod of length $$40$$ $$mm.$$ Subsequently, it is compressed to make a rod of final length $$10$$ $$mm.$$ Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

A strip of $$120mm$$ width and $$8mm$$ thickness is rolled between two $$300$$ $$mm$$-diameter rolls to get a strip of $$120mm$$ width and $$7.2mm$$ thickness. The speed of the strip at the exit is $$30m/min.$$ There is no front or back tension. Assuming uniform roll pressure of $$200$$ $$MPa$$ in the roll bite and $$100\% $$ mechanical efficiency, the minimum total power (in $$kW$$) required to drive the two rolls is ____________________