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A uniform rope of linear mass density la...

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.

Text Solution

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The correct Answer is:
`(lambdaLg)/4`
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Knowledge Check

  • A uniform rope of length l and mass m lies on a smooth horizontal table with its length perpendicular to the edge of the table and a small part of the rope having over the edge. The rope starts sliding from rest under the weight of the over hanging end. The velocity of the rope when the length of the hanging part is . x

    A
    ` sqrt((gx)/l)`
    B
    `sqrt((gx^(2))/l)`
    C
    `(gx)/l`
    D
    `(gx^(2))/l`

  • A uniform rope of linear mass density lambda and length l is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the ground is :-

    A
    `(1)/(2)lambdalv^(2) + (lambdal^(2)g)/(2)`
    B
    `lambdalgv`
    C
    `(1)/(2)lambdav^(3) + (lambdalvg)/(2)`
    D
    `lambdalgv + (1)/(2)lambdav^(3)`

  • A uniform rope of their mass density lamda and length l is coiled on smooth horizontal surface. One end is pulled up by an external agent wit consant vertical velocity v . Choose the correct option(s)

    A
    Power developed by external agent as a function of `x` is `P=lamdaxgv`
    B
    Power developed by external agent as a function of `x` is `P=(lamdav^(2)+lamdaxg)v`
    C
    Energy lost during the complete lift of the rope is zero
    D
    Energy lost during the complete lift of the rope is `(lamdalv^(2))/2`

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