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A ring of radius R is made of a thin wir...

A ring of radius R is made of a thin wire of material of density `rho`, having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is `omega`.
The ratio of kinetic energy to potential energy is

A

`(Y)/(pR^2omega^2)`

B

`(2Y)/(pR^2omega^2)`

C

`(Y)/(2pR^2omega^2)`

D

`(Y)/(4pR^2omega^2)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • A ring of radius R is made of a thin wire of material of density rho , having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is omega . The tension in the ring will be

    A
    `(arhoR^(2)omega^(2))/(2)`
    B
    `a rho R^(2) omega^(2)`
    C
    `2a rho R^(2) omega^(2)`
    D
    `(arhoR^(2) omega^(2))/(4)`

  • A ring of radius R is made of a thin wire of material of density rho having cross section area a. The ring rotates with angular velocity omega about an axis passing through its centre and perpendicular to the plane. If we consider a small element of the ring,it rotates in a circle. The required centripetal force is provided by the component of tensions on the element towards the centre. A small element of length dl of angular width d theta is shown in the figure. If T is the tension in the ring, then

    A
    `T=(a rho R^(2)omega^(2))/(2)`
    B
    `T=a rho R^(2) omega^(2)`
    C
    `a^(2) rho omega^(2)`
    D
    `T=2arho R^(2) omega^(2)`

  • A ring of radius R is made of a thin wire of material of density rho having cross section area a. The ring rotates with angular velocity omega about an axis passing through its centre and perpendicular to the plane. If we consider a small element of the ring,it rotates in a circle. The required centripetal force is provided by the component of tensions on the element towards the centre. A small element of length dl of angular width d theta is shown in the figure. The centripetal force acting on the element is

    A
    `(a.rhodlomega^(2)R)`
    B
    `R^(2) d theta.omega^(2)`
    C
    `(1)/(2)a rho d l omega^(2) R`
    D
    zero

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