A wire of length $$\mathrm{L}$$ and radius $$\mathrm{r}$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$\mathrm{F}$$, its length increases by $$5 \mathrm{~cm}$$. Another wire of the same material of length $$4 \mathrm{L}$$ and radius $$4 \mathrm{r}$$ is pulled by a force $$4 \mathrm{F}$$ under same conditions. The increase in length of this wire is __________________ $$\mathrm{cm}$$.

A unit scale is to be prepared whose length does not change with temperature and remains $$20 \mathrm{~cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $$40 \mathrm{~cm}$$ and length of iron will be __________ $$\mathrm{cm}$$. $$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right.$$ and $$\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} \mathrm{~K}^{-1}\right)$$.

The volume charge density of a sphere of radius $$6 \mathrm{~m}$$ is $$2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$\times 10^{10} \,\mathrm{NC}^{-1}$$.

[Given : Permittivity of vacuum $$\epsilon_{0}=8.85 \times 10^{-12} \,\mathrm{C}^{2}\, \mathrm{~N}^{-1}-\mathrm{m}^{-2}$$ )

In the given figure, the value of V_o will be _____________ V.