Question

When a thin hollow sphere rolls without slipping on a flat surface, the fraction of its total energy associated with rotation is ______.

Options

• `1/2`

• `2/5`

• `3/5`

• `2/3`

Answer 1

When a thin hollow sphere rolls without slipping on a flat surface, the fraction of its total energy associated with rotation is `bbunderline(2/5)`.

Explanation:

For a thin spherical shell, `k^2/R^2 = 2/3`, so that total energy,

E = `1/2 Mv^2 (1 + k^2/R^2)`

= `1/2 Mv^2 (1 + 2/3)`

= `5/6 Mv^2`

`E_(rot) = 1/2 Iω^2`

= `1/2(2/3 MR^2)ω^2`

= `1/3 Mv^2`

∴ `E_(rot)/E = (1//3)/(5//6)`

= `2/5`