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