A uniform rope of linear mass density `lambda` (kg/m) passes over a smooth pulley of negligible dimension. At one end B of the rope there is a small particle having mass one fifty of the rope. Initially the system is held at rest with length L of the rope on one side and length `L/4` on the other side of the pulley (see fig). The external agent begins to pull the end A downward. Find the minimum work that the agent must perform so that the small particle will definitely reach the pulley.

A uniform rope of linear mass density `lambda` (kg/m) passes over a sm

1.	A uniform rope of linear mass density `lambda` (kg/m) passes over a smooth pulley of negligible dimension. At one end B of the rope there is a small particle having mass one fifty of the rope. Initially the system is held at rest with length L of the rope on one side and length `L/4` on the other side of the pulley (see fig). The external agent begins to pull the end A downward. Find the minimum work that the agent must perform so that the small particle will definitely reach the pulley.
Answer» Correct Answer - `(lambdaLg)/4`

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