Physics - Rotation Question with Solution | TestHub

Due to pure rolling${\text{E}}_{t=0}={\text{E}}_{t=1}$

$\text{I}=\frac{{\text{MR}}^2}{2}$

${\text{V}}_{\text{cm}}=\omega \text{R}$

${\text{E}}_{\text{t}=0}=\frac{1}{2}{\text{MV}}_{\text{cm}}^2+\frac{1}{2}{\text{I}}_{\text{cm}}{\omega }^2$

$\frac{1}{2}\text{M}{\omega }^2{\text{R}}^2+\frac{1}{2}\frac{{\text{MR}}^2}{\text{2}}\times {\omega }^2$

$\frac{1}{2}\times \frac{3}{2}\text{M}{\omega }^2{\text{R}}^2$

${\text{E}}_{\text{t}=\text{T}}=\frac{1}{2}{\text{kx}}^2$

$\frac{1}{2}\times \frac{3}{2}\text{M}{\omega }^2{\text{R}}^2=\frac{1}{2}{\text{kx}}^2$

$\text{x}=\omega \text{R}\sqrt{\frac{3\text{M}}{2k}}$