Hello Student,

These questions can be easily solved using work energy theorem,

Which States : Work done by external torque on rotating a body is equal to change in rotational kinetic energy.

Now ,

Mgsin(x)*R = I(alpha) = (Mr^2 + Mk^2)a/R

Using the above equation we can derive the following :

Acceleration = gsin(x)/1+(k^2/r^2)

Velocity = {2gh/1+(k^2/r^2)}^1/2

[x = angle of inclination . h = height from which sphere starts rolling , k= radius of gyration , r = radius of the sphere , alpha = angular acceleration]

Velocity can be found out using the above formula.