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String is wrapped on a cylinder and free...

String is wrapped on a cylinder and free end of the string is pulled by a man as shown in figure. Horizontal surface is sufficiently rough. Person pulls `l_(1)` length of string and centre of the cylinder is found to move by a distance `l_2`. Calculate `l_(1)//l_(2)`.

Text Solution

Verified by Experts

The correct Answer is:
2
String is passing over the top point. When cylinder performs pure rolling then we know that speed of the top point is two times the speed of the centre of cylinder. Hence there will be same ratio for the distances involved
`(l_(1))/(l_(2))=2`
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Knowledge Check

  • A string is wrapped around a cylinder of mass M and radius R . The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder upwinds the string. The tension in the string is:

    A
    `2Mg//3`
    B
    `Mg//2`
    C
    `Mg//3`
    D
    `Mg//6`

  • A string is wrapped around a cylinder of mass M and radius R . The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string. The tension in the string is

    A
    `(Mg)/6`
    B
    `(Mg)/3`
    C
    `(Mg)/2`
    D
    `(2Mg)/3`

  • A string wrapped around a cyliner of mass m and radius R . The end of the string is connected to block of same mass hanging vertically. No friction exists between the horizontal surface and cylinder. Acceleration of cylinder is:

    A
    `g`
    B
    `g/2`
    C
    `g/4`
    D
    `(3g)/4`