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A uniform rope of length l and mass m li...

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`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • A uniform chain of length L lies on a smooth horizontal table with its length perpendicular to the edge of the table and a small portion of the chain is hanging over the edge. The chain starts sliding due to the weight of the hanging part

    A
    The acceleration of the chain is `(gx//L)`, where x is the length of the hanging part of chain.
    B
    The acceleration of the chain is `(g//L)(L-x)`, where x is the length of hanging part of chain.
    C
    The velocity of the chain is `x sqrt((g)/(L))`, where x is the length of hanging part of chain.
    D
    The velocity of the chain is `(L-x) sqrt((g)/(L))`, where x is the length of hanging part of chain.

  • A uniform rope of length 'L and linear density 'mu' is on a smooth horizontal table with a length 'I' lying on the table. The wrok done in pulling the hanging part on to the table is

    A
    `(mu g(L-l)^(2))/(2)`
    B
    `(mu g(L-l)^(2))/(2l^(2))`
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    `(mu g L)/(2(L-l))`

  • A uniform chain of length l and mass m is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is :

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    B
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    C
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    D
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