Question

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Class 11th

Sub. => Physics

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Que. A heavy a uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one is of the table is??

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Jai bajarang bali

@DrS.M.

Answer 1

This is fairly an easy question, if you understand the concept of Mass Gradient, which in itself is natural and intuitive. I will show the working of the solution for the problem in following steps:

Step 1: Assume total length of the chain to be = L. The length of the portion hanging = x. The remaining part = L-x

Step 2: Since the chain is uniform, its mass gradient is constant throughout its length. Its mass gradient = M/L.

Step 3: The gravitational force on the hanging part = mg = (M/L)xg. This is the force acting on the part of the chain resting on the table top. Draw its free-body diagram, showing all the forces acting on it, including Normal force and Frictional force.

Step 4: Since the gravitational force and normal force cancel out each other, the body stays in equilibrium along Y-axis. All you must check for is the condition for horizontal equilbrium. For this, the force acting on resting part due to hanging part, and the frictional force must balance each other. This is the major part of the problem done, with just some analytical thinking.

Step 5: Now comes the working part,

(M/L)xg = k (M/L)(L-x)g

i.e., Force due to hanging part = Frictional force

Now, value of frictional constant k is given to be 0.25, which would give us-

x = (k/k+1)L

→ x = L/5

Therefore, one-fifth of the chain would be hanging from the table.

Answer 2

your answer to this question is in the pic,