In figure, a sphere of radius 2m rolls on a plank. The value of α=___________ rad/sec² (where $\mathrm{\alpha }$ is angular acceleration)

As sphere is rolls, the lowest point of the sphere should have the same acceleration as the plank. Hence, ${\mathrm{a}}_1=\mathrm{\alpha R}-{\mathrm{a}}_2\Rightarrow 2=2\mathrm{\alpha }-4\Rightarrow \mathrm{\alpha }=3\mathrm{rad}/{\mathrm{s}}^2$