A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.

width of the plate $$w = 200$$ $$mm,$$ thickness of the plate $$t = 5$$ $$mm,$$ number of rivets $$n = 3,$$ diameter of the rivet $${d_r} = 10\,\,\,mm,$$ diameter of the rivet hole $${d_h} = 11\,\,\,mm,$$ allowable tensile stress of the plate $${\sigma _p} = 200\,\,MPa,$$ allowable shear stress of the rivet $${\sigma _s} = 100\,\,MPa$$ and allowable bearing stress of the rivet $${\sigma _c} = 150\,\,MPa.$$

If the plates are to be designed to avoid tearing failure, the maximum permissible load $$P$$ in $$kN$$ is

A cube shaped casting solidifies in $$5$$ min. The solidification time in min for a cube of the same material, which is $$8$$ times heavier than the original casting, will be

In a rolling process, the state of stress of the material undergoing deformation is

In orthogonal turning of a bar of $$100$$ $$mm$$ diameter with a feed of $$0.25$$ $$min/rev,$$ depth of cut of $$4$$ $$mm$$ and cutting velocity of $$90$$ $$m/min,$$ it is observed that the main (tangential) cutting force is prependicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is $$1500$$ $$N.$$

The normal force acting at the chip-tool interface in $$N$$ is