Question

assuming the length of a chain to be L and coefficient of static friction Mu, compute the maximum length of the chain which can be held outside a table without slipping.​

Answer 1

Answer:x=u÷u+1×L

where,u=coefficient of static friction

Explanation:

Let the total length of chain be L

Length of portion hanging be x

Remaining part=L-x

Whenever we use the concepts of objects like chain or rod whose linear mass densities are constant we should use the concept of mass gradient i.e M/L

F=mg=M/L×g

Since the gravitational force and normal force cancel out each other we balance the horizontal forces

Frictional force=gravitational force on hanging part

u×(M/L)×(L-x)×g=(M/L)×g

x=(u/u+1)L