In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\, + 180\,\,MPa,\,\,\,$$ $${\sigma _2} = \,\, - 100\,\,MPa,\,\,\,$$ $${\sigma _3} = 0.$$ Following Von Mises' criterion, the yield stress is _____________ $$MPa.$$

In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

Two cutting tools with tool life equations given below are being compared:
$$\eqalign{ & Tool\,\,1:\,\,\,\,\,\,\,V{T^{0.1}} = 150 \cr & Tool\,\,2:\,\,\,\,\,\,\,V{T^{0.3}} = 300 \cr} $$
where $$V$$ is cutting speed in $$m/minute$$ and $$T$$ is tool life in minutes. The breakeven cutting speed beyond which Tool $$2$$ will have a higher tool life is _______________ $$m/minute$$.

Metric thread of $$0.8$$ $$mm$$ pitch is to be cut on a lathe. Pitch of the lead screw is $$1.5$$ $$mm.$$ If the spindle rotates at $$1500$$ $$rpm,$$ the speed of rotation of the lead screw $$(rpm)$$ will be _____________