Young's modules of material of a wire of length '$$L$$' and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

The gravitational potential at a point above the surface of earth is $$-5.12 \times 10^7 \mathrm{~J} / \mathrm{kg}$$ and the acceleration due to gravity at that point is $$6.4 \mathrm{~m} / \mathrm{s}^2$$. Assume that the mean radius of earth to be $$6400 \mathrm{~km}$$. The height of this point above the earth's surface is :

The horizontal component of earth's magnetic field at a place is $$3.5 \times 10^{-5} \mathrm{~T}$$. A very long straight conductor carrying current of $$\sqrt{2} \mathrm{~A}$$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is __________ $$\times 10^{-6} \mathrm{~N} / \mathrm{m}$$.

Two cells are connected in opposition as shown. Cell $$\mathrm{E}_1$$ is of $$8 \mathrm{~V}$$ emf and $$2 \Omega$$ internal resistance; the cell $$\mathrm{E}_2$$ is of $$2 \mathrm{~V}$$ emf and $$4 \Omega$$ internal resistance. The terminal potential difference of cell $$\mathrm{E}_2$$ is __________ V.