Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is ___________ (rounded off to 2 decimal places).

Assume that solidification time follows Chvorinov's rule with an exponent of 2 .

Cylindrical workpieces of diameter 60 mm and length 400 mm are machined on a lathe at a cutting speed of $25 \mathrm{~m} \mathrm{~min}^{-1}$ and a feed of $0.2 \mathrm{~mm} \mathrm{rev}^{-1}$. The Taylor's tool life parameters $C$ and $n$ for this setup are 75 and 0.25 , respectively. The tool changing time is 3 minutes. With a labor and overhead cost of Rs. 5 per minute, the tool changing cost per piece is Rs. ___________ (rounded off to 2 decimal places).

The yield stress of a metal in uniaxial tension is 200 MPa . According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

A metallic square plate is subjected to a uniform hydrostatic pressure $(P)$. Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below.

For the Mohr's circle, normal stress is positive towards right and shear stress is positive in the upward direction.