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A thin hollow sphere of mass m is comple...

A thin hollow sphere of mass `m` is completely filled with non viscous liquid of mass `m`. When the sphere roll-on horizontal ground such that centre moves with velocity `v`, kinetic energy of the system is equal to

A

`mv^(2)`

B

`(4)/(3)mv^(2)`

C

`(4)/(5)mv^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Viscous liquid has only translational kinetic energy
`thereforeKE=` translational `+` rotaional kinetic energy
of hollow sphere `+` translational kinetic energy of liquid
`=(1)/(2)mv^(2)+(1)/(2)xx(2)/(3)mR^(2)((v)/(R))^(2)+(1)/(2)mv^(2)`
`=(4)/(3)mv^(2)`
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Knowledge Check

  • A thin hollow sphere of mass m is completely filled with a liquid of mass m . What the sphere rolls with a velocity v, kinetic energy of the system is (neglect friciton)

    A
    `(1)/(2)mv^(2)`
    B
    `mv^(2)`
    C
    `(4)/(3)mv^(2)`
    D
    `(4)/(5) mv^(2)`

  • A hollow sphere of radius R and mass m fully filled with water of mass m . It is rolled down a horizontal plane such that its centre of mass moves with a velocity v . If it purely rolls.

    A
    Kinetic energy of the sphere is `(5)/(6) mv^(2)`
    B
    Kinetic energy of the sphere is `(4)/(5) mv^(2)`
    C
    Angular momentum of the sphere about a fixed point on ground is `(8)/(2) mvR`
    D
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  • A massless thin hollow sphere is completely filled with water of mass m . If the hollow sphere rolls with a velocity v . The kinetic energy of the sphere of water is : (Assume water is non viscous)

    A
    `1/2 mv^(2)`
    B
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    C
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    D
    `5/6 mv^(2)`

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