:

Let be mass of the block and be length of the inclined plane.

According to work‐energy theorem

(Initial and final speeds are zero) Work done by friction Work done by gravity

;

Alternate Solution:

For upper half smooth plane

Acceleration of the block, Here, (block starts from rest)

Using, , we have

For lower half rough plane

Acceleration of the block, where is the coefficient of friction between the block and lower half of the plane

Here,

(block comes to rest)

Again, using , we have

or