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A wheel rolls without slipping on a hori...

A wheel rolls without slipping on a horizontal surface such that its velocity of center of mass is `v`. The velocity of a particle at the highest point of the rim is

A

zero

B

`v`

C

`2 v`

D

`sqrt2 v`

Text Solution

Verified by Experts

When a body rolls without slipping, the velocity of any point of the body is resultant of two velocities: one due to pure translational motion and another due to pure rotational motion. Also, `v=romega`.
`v_(A)=v+R omega=v+v=2v`
`v_(B)=sqrt(v^(2)+(romega)^(2))=sqrt2v`
`v_(C)=v-v=0`
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Knowledge Check

  • Assertion: A disc rolls without slipping on a horizontal surface and the linear speed of its centre of mass is v. The rotational speed of the particles on its rim at the top of the disc will be 2v. Reason: The disc rolls as if it is rotating about the point of contact with the horizontal surface.

    A
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    B
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    C
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    D
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  • If the velocity of centre of mass of a rolling body is V then velocity of highest point of that body is

    A
    `sqrt(2)V`
    B
    `V`
    C
    `2V`
    D
    `V/(sqrt(2))`

  • If V is velocity of centre of mass of a rolling body then velocity of lowest point of that body is

    A
    `sqrt(2)V`
    B
    `V`
    C
    `2V`
    D
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