KVPY SX SB Exam 20141 Question Paper

Initial sphere is slipping and finally it start rolling. During its motion τ about point of contact is zero.
∴ Angular momentum of sphere about point of contact remain conserved. $\mathit{I}\mathit{\omega }=\left(\mathit{I}+\mathit{M}{\mathit{R}}^2\right)\mathit{\omega }\prime$
$\frac{2}{5}\mathit{M}{\mathit{R}}^2\mathit{\omega }=\left(\frac{2}{5}\mathit{M}{\mathit{R}}^2+\mathit{M}{\mathit{R}}^2\right)\mathit{\omega }\prime$
$\mathit{\omega }\prime =\frac{2\mathit{\omega }}{7}$