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 ___________

The following data is applicable for a turning operation. The length of job is $$900$$ $$mm,$$ diameter of job is $$200$$ $$mm,$$ feed rate is $$0.25$$ $$mm/rev$$ and optimum cutting speed is $$300$$ $$m/min.$$ The machining time (in $$min$$) is _____________

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

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 _______.

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