A uniform chain of length L is lying partly on a table, the remaining part hanging down from the edge of the table. If the coefficient of friction between the chain and the table is 0.5 what is the minimum length of the chain that should lie on the table, to prevent the chain from slipping down to the ground.

Explanation

To solve the problem, we need to determine the minimum length of the chain that must lie on the table to prevent it from slipping off. We will denote the total length of the chain as \( L \) and the length of the chain on the table as \( l \). The length of the chain hanging off the table will then be \( L - l \).

### Step-by-Step Solution:

1. **Identify Forces Acting on the Chain:**
- The weight of the hanging part of the chain, which is \( m_2g \) where \( m_2 \) is the mass of the hanging part and \( g \) is the acceleration due to gravity.
- The normal force acting on the part of the chain on the table, which is \( m_1g \) where \( m_1 \) is the mass of the part of the chain lying on the table.
- The frictional force opposing the downward motion, which is given by \( f = \mu R \) where \( \mu \) is the coefficient of friction (0.5) and \( R \) is the normal force.
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