The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

Question

Dr. Abubacker · Accepted Answer

[Solution from source] Let the plane length be L. Gain in KE from gravity over the full length, mg sin θ·L, must equal the friction work on the rough lower half, μ mg cos θ·(L/2). This gives μ = 2 tan θ. μ = tan θ would only stop the acceleration on the rough part, not bring the block to rest. Answer (3).

Q. The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

Explanation

Reviewed by Dr. Abubacker

Want to attempt the full paper?