Question

Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ______.

Options

• `2/5`

• `2/7`

• `1/5`

• `7/10`

Answer 1

Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is `underlinebb(2/7)`.

Explanation:

Here v_cm = ωR

K_rot = `1/2"I"_"cm"omega^2`

= `1/2xx2/5"mR"^2xxomega^2`

= `1/5"mv"_"cm"^2`

`"K"_"trans"=1/2"mv"_"cm"^2`

∴ `"K"_"rot"/"K"_"total"=(1/5"mv"_"cm"^2)/(1/5"mv"_"cm"^2+1/2"mv"_"cm"^2)`

= `(1/5)/(7/10)`

= `2/7`