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

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times {10^{ - 2}}\,\,N$$ (see figure). The length of the slider is $$30$$ $$cm$$ and its weight negligible. The surface tension of the liquid film is