A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10^{-3} \mathrm{~J}$$. The speed of the centre of mass of the sphere is __________ $$\operatorname{cm~s}^{-1}$$

Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$$. The electric flux through the cube of side $$20 \mathrm{~cm}$$ when placed in electric field (as shown in the figure) is __________ $$\mathrm{V} \mathrm{~cm}$$.

A thin rod having a length of $$1 \mathrm{~m}$$ and area of cross-section $$3 \times 10^{-6} \mathrm{~m}^{2}$$ is suspended vertically from one end. The rod is cooled from $$210^{\circ} \mathrm{C}$$ to $$160^{\circ} \mathrm{C}$$. After cooling, a mass $$\mathrm{M}$$ is attached at the lower end of the rod such that the length of rod again becomes $$1 \mathrm{~m}$$. Young's modulus and coefficient of linear expansion of the rod are $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$ and $$2 \times 10^{-5} \mathrm{~K}^{-1}$$, respectively. The value of $$\mathrm{M}$$ is __________ $$\mathrm{kg}$$.

(Take $$\mathrm{g=10~m~s^{-2}}$$)

In a medium the speed of light wave decreases to $$0.2$$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $$x: 1$$. The value of $$x$$ is _________.

(Given speed of light in free space $$=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$$ and for the given medium $$\mu_{\mathrm{r}}=1$$)