Gray cast iron blocks of size $$100\,\,mm \times 50\,\,mm \times 10\,\,mm$$ with a central spherical cavity of diameter $$4$$ mm are sand cast. The shrinkage allowance for the pattern is $$3\% $$. The ratio of the volume of the pattern to volume of the casting is ___________________

The value of true strain produced in compressing a cylinder to half its original length is

The voltage - length characteristic of a direct current arc in an arc welding process is $$V=$$ $$(100+40l),$$ where $$l$$ is the length of the arc in $$mm$$ and $$V$$ is arc voltage in volts. During a welding operation, the arc length varies between $$1$$ and $$2$$ $$mm$$ and the welding current is the range $$200$$-$$250A$$. Assuming a linear power source, the short circuit current is _____________$$A.$$

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 ___________