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

Kinetic energy K for a rolling sphere without slipping is given by 

$\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}{\mathrm{I\omega }}^2$

$\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}\left(\frac{2}{5}{\mathrm{mR}}^2\right){\left(\frac{\mathrm{v}}{\mathrm{R}}\right)}^2$

From the K.E given in question and above equation

$\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2\left[1+\frac{2}{5}\right]=7\times {10}^{-3}$

$\frac{7}{10}\times \left(1\right)\times {\mathrm{v}}^2=7\times {10}^{-3}$

$\therefore \mathrm{v}=10\mathrm{cm}/\mathrm{s}$