For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is a constant, $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in minutes. The Taylor's tool life equation is $$V{T^{0.25}} = 150.$$ The cutting speed (in $$m/min$$) for the minimum total cost is ___________

For the situation shown in the figure below the expression for $$H$$ in terms of $$r, R$$ and $$D$$ is

A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200^oC, the axial stress developed in the rod is __________ MPa.

Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10⁻⁵ per ^oC.

In the figure, the load P = 1 N, length L = 1 m, Young’s modulus E = 70 GPa, and the cross-section of the links is a square with dimension 10 mm $$ \times $$ 10 mm. All joints are pin joints.

The stress (in Pa) in the link AB is _______.

$$(Indicate\,\,compressive\,\,stress\,\,by\,\,a\,\,negative\,$$
$$\,sign\,\,and\,\,tensile\,\,stress\,\,by\,\,a\,\,positive\,\,sign)$$