During the measurement of internal taper of a part using standard balls of diameter $$15$$ $$mm$$ and $$20$$ $$mm$$, the large ball is found to protrude by $$5$$ $$mm$$ $$\left( {{h_1}} \right)$$ and the top of small ball is found to be $$35$$ $$mm$$ $$\left( {{h_2}} \right)$$ below the top face of the gauge. The taper angle, in degree, is ________________.

A surface is prepared specially for an application with the profile as shown in the figure.

The theoretical $${R_a}$$ value for this surface, in $$\mu m,$$ is _______________.

The room-temperature stress $$\left( \sigma \right)$$ - strain $$\left( \varepsilon \right)$$ curves of four materials $$P, Q, R$$ and $$S$$ are shown in the figure below. The material that behaves as a rigid perfectly plastic material is

A metallic bar of uniform cross-section with specific weight of $$100$$ kN/m³ is hung vertically down. The length and Young's modulus of the bar are $$100$$ m and $$200$$ GPa, respectively. The elongation of the bar, in mm, due to its own weight is __________ .