Question

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 ___$cm s ^{-1}$

Answer 1

$ \frac{1}{2} mv ^2+\frac{1}{2} I \omega^2=7 \times 10^{-3}$
$ \frac{1}{2} mv ^2+\frac{1}{2}\left(\frac{2}{5} MR ^2\right)\left(\frac{ V }{ R }\right)^2=7 \times 10^{-3} $
$ \frac{1}{2} MV ^2\left[1+\frac{2}{5}\right]=7 \times 10^{-3} $
$ \frac{1}{2}(1)\left( V ^2\right)\left(\frac{7}{5}\right)=7 \times 10^{-3}$
$ V ^2=10^{-2} $
$ V =10^{-1}=0.1\, m / s =10 \,cm / s$