The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by $${100^ \circ }C$$ is: (For steel Young's modulus is $$2 \times {10^{11}}\,\,N{m^{ - 2}}$$ and coefficient of thermal expansion is $$1.1 \times {10^{ - 5}}\,{K^{ - 1}}$$ )

An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $$=76$$ $$cm$$ of $$Hg$$)

A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $$\sigma $$ at equilibrium position. The extension $${x_0}$$ of the spring when it is in equilibrium is:

If a piece of metal is heated to temperature $$\theta $$ and then allowed to cool in a room which is at temperature $${\theta _0},$$ the graph between the temperature $$T$$ of the metal and time $$t$$ will be closest to