Home
Class 11
PHYSICS
A thin ring of radius R is made of a wir...

A thin ring of radius R is made of a wire of density `rho` and Young’s modulus Y. It is spun in its own plane, about an axis through its centre, with angular velocity w. Determine the amount (assumed small) by which its circumference increases.

Text Solution

Verified by Experts

The correct Answer is:
`(2pi rho R^(3) omega^(2))/(Y)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A thin ring of radius R is made of a material of density rho and Young's modulus Y. If the ring is rotated about its centre in its own plane with angular velocity omega , find the small increases in its radius.

A thin ring of radius R is made of a material of density rho is Young's modulus Y . If the ring is rotated about its centre in its own plane with anglular velocity omega , if the small increase in its radius is (2rhoomega^(3)R^(3))/(lambdaY) then find lambda .

Knowledge Check

  • Very thin ring of radius R is rotated about its centre. Its radius will

    A
    increase
    B
    decrease
    C
    change depends on material
    D
    none of the above

  • Radius of gyration of a ring about a transverse axis passing through its centre is

    A
    `0.5xx` diameter of ring
    B
    diameter of ring
    C
    `2xx` diameter of ring
    D
    `"(diameter of ring)"^(2)`

  • 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)`

    • Similar Questions

    Explore conceptually related problems

    A solid sphere of radius r and mass m rotates about an axis passing through its centre with angular velocity omega . Its K.E . Is

    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

    The M.I. of the solid sphere of density 'rho' and radius 'R' about an axis passing through its centre is given by

    Moment of inertia of a circular ring about an axis through its centre and perpendicular to its plane is

    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

    Home
    Profile