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Prove the result that the velocity v of ...

Prove the result that the velocity `v` of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^(2) = (2gh)/((1 + k^(2)//R^(2))` using dynamical consideration (i.e. by consideration of forces and torque). Note k is the radius of gyration of the body about its symmetry axis, and `R` is the radius of the body. The body starts from rest at the top of the plane.

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Step by step text solution for Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^(2) = (2gh)/((1 + k^(2)//R^(2)) using dynamical consideration (i.e. by consideration of forces and torque). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane. by PHYSICS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclied plane of a hight h is given by v^(2) = (2gh)/((1 + k^(2)//R^(2)) using dynamical consideration (i.e. by consideration of forces and torque). Note k i sthe radius of gyration of the body about its symmentry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

The radius of gyration of a disc about its own axis is is R/sqrt(2) The radius of gyration about its diameter is- - - - -

Knowledge Check

  • The radius of gyration of a sphere of radius R about a tangent is.

    A
    `(sqrt(2))/(3) R`
    B
    `(sqrt(2))/(5) R`
    C
    `sqrt((5)/(3)) R`
    D
    `sqrt((7)/(5)) R`

  • The radius of gyration of a solid sphere of radius R about its tangential is

    A
    `sqrt((7)/(5))R`
    B
    `sqrt((2)/(5))R`
    C
    `sqrt((5)/(7))`
    D
    `R`

  • The radius of of disc is 2 m the radius of gyration of disc about an axis passing through its diameter is

    A
    2 m
    B
    2 cm
    C
    1 m
    D
    0.2 m

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