Question

A mass m slides down a plane inclined at an angle $\alpha$ to the horizontal. The height of the inclined plane is h and the coefficient of friction over both surface is $\mu$. Then the distance that it will move on the horizontal plane after covering the entire length of the inclined plane.

• A. h- $\frac{h}{tan\alpha }$
• B. $\frac{h}{\mu }$ - $\frac{h}{tan\alpha }$
• C. $\frac{h}{\mu }$ - h
• D. $\frac{h}{\mu }$ - $\frac{1}{tan\alpha }$

Answer 1

The correct option is B $\frac{h}{\mu }$ - $\frac{h}{tan\alpha }$

Block starts from A and comes to rest again at C. Along the path, loss in potential energy = work done against friction.

mgh = WAB + WBC = $\mu$mg cos $\alpha$. h/sin$\alpha$ + $\mu$mg l

or l = $\frac{h}{\mu }$ - $\frac{h}{tan\alpha }$