A mass m slides down a fixed plane inclined at an angle a to the horizontal plane after covering the entire length of the inclined plane. The height of the inclined plane is h and the coefficient of friction over both surfaces is `mu`.

Explanation

Block starts from A and comes to rest at C. Along the path, loss in GPE = work done against friction on inclined plane and horizontal plane.

`mgh = W_(AB) + W_(BC)`
`mgh = (mu mg cos alpha) AB + (mu mg) BC`
` mgh = (mumg cos alpha) (h)/(sin alpha)+ mu mgL`
`muL = h - mu cot alpha`
`Rightarrow L = h(1/mu - cot alpha)`