Out of the two spheres of equal mass one rolls down a smooth inclined plane while other is freely falling both from same height . in which case is the work done more? why?

In case of sphere rolls down a smooth inclined plane , work is done by gravity only as in free fall but as it is inclined

So, there comes a factor sin( angle of inclination)

So acceleration becomes g sin( angle of inclination)

Now , As in free fall acceleration is g

And max value of Sin is 1

So ,range of acceleration in smooth inclined plane varies from 0 to g

that is max acceleration or max work done as Work = m × acceleration × displacement

= mg sin ( angle) × displacement

As sin( angle) = height/displacement

So it becomes mg× height

In free fall, Work done = mg × height

So, Free fall work done is same as work done in smooth inclined plane

So, Work done in free fall = work done in smooth inclined plane