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A thin hollow cylinder open at both ends...

A thin hollow cylinder open at both ends
(i) Slides without rotating
(ii) Rolls without slipping, with the same speed.
The ratio of kinetic energies in the two cases is

A

`1:1`

B

`4:1`

C

`1:2`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
C
Translational K.E. =`1/2mv^(2)`
K.E. of rolling body= K.E. of translation+ K.E. of rotation
`E=1/2mv^(2)+1/2Iomega^(2)=1/2mv^(2)+1/2mR^(2).omega^(2)`
`E=1/2mv^(2)+1/2mv^(2)=mv^(2)`
`therefore("Translation K.E.")/(.Total K.E.")=1/2.(mv^(2))/(mv^(2))=1/2`
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Knowledge Check

  • A thin hollow cylinder open at both ends: (i) Slides without rotating (ii) Rolls without slipping, with the same speed. The ratio of kinetic energy in the two cases is

    A
    `1:1`
    B
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    C
    `1//4`
    D
    `3//4`

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    A
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    B
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    C
    1
    D
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