The maximum elongation of a steel wire of $$1 \mathrm{~m}$$ length if the elastic limit of steel and its Young's modulus, respectively, are $$8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$$ and $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$, is:

A thin flat circular disc of radius $$4.5 \mathrm{~cm}$$ is placed gently over the surface of water. If surface tension of water is $$0.07 \mathrm{~N} \mathrm{~m}^{-1}$$, then the excess force required to take it away from the surface is

A metallic bar of Young's modulus, $$0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$ and coefficient of linear thermal expansion $$10^{-5}{ }^{\circ} \mathrm{C}^{-1}$$, length $$1 \mathrm{~m}$$ and area of cross-section $$10^{-3} \mathrm{~m}^2$$ is heated from $$0^{\circ} \mathrm{C}$$ to $$100^{\circ} \mathrm{C}$$ without expansion or bending. The compressive force developed in it is :

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $$100 \mathrm{~cm}$$ to stretch it by $$1 \mathrm{~mm}$$ is (if Young's modulus of the wire $$=2.0 \times 10^{11} \mathrm{Nm}^{-2}$$ ) :