Explanation:
Let a is the linear acceleration of the descending sphere. It is given by,
[tex]a=\dfrac{dv}{dt}[/tex].......(1) (change in velocity)
Let [tex]\alpha[/tex] is the angular acceleration α of the rotating wheel. It is given by :
[tex]\alpha =\dfrac{d\omega}{dt}[/tex]............(2) (change in angular velocity)
Dividing equation (1) and (2) we get :
[tex]\dfrac{a}{\alpha }=\dfrac{dv}{d\omega}[/tex]
Since, [tex]v=r\omega[/tex]
[tex]\dfrac{a}{\alpha }=\dfrac{d(r\omega)}{d\omega}[/tex]
[tex]\dfrac{a}{\alpha }=r[/tex]
[tex]a=\alpha r[/tex]
[tex]a=\alpha \times r[/tex]
Hence, this is the required solution.
