A uniform chain is placed at rest on a rough surface of base length l and height h on an irregular surface as shown. Then, the minimum coefficient of friction between the chain and the surface must be equal to n(h/l). Find n = ?
Physics · Mixed Chapter
JEE Mains

Question

A uniform chain is placed at rest on a rough surface of base length l and height h on an irregular surface as shown. Then, the minimum coefficient of friction between the chain and the surface must be equal to n(h/l). Find n = ?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For the uniform chain at rest along the irregular rough surface, gravitational potential-energy decrease for an infinitesimal downhill shift dx is (M g)(h/l)dx, corresponding to the average slope h/l. Step 2: The maximum available static-friction work for that displacement in the ideal limiting model is μMg dx. Step 3: At limiting equilibrium μMg dx = Mg(h/l)dx, so μₘᵢₙ=h/l. Step 4: Given μₘᵢₙ=n(h/l), n=1. Answer: 1. (Uses the standard ideal uniform-chain force-balance assumption.)