In figure, a sphere of radius 2m rolls on a plank. The value of α is (where α is angular acceleration)

As sphere rolls, the lowest point of the sphere should have the same acceleration as the plank

Hence, ${\mathrm{a}}_1=\mathrm{\alpha R}-{\mathrm{a}}_2\Rightarrow 2=2\mathrm{\alpha }-4$

$\Rightarrow \mathrm{\alpha }=3\mathrm{rad}/{\sec }^2$