A uniform sphere of mass `500 g` rolls without slipping on a plane surface so that its centre moves at a speed of `0.02 m//s`.
The total kinetic energy of rolling sphere would be (in `J`)

Options

A. `1.4 xx 10^(-4)J`
B. `0.75 xx 10^(-3)J`
C. `5.75 xx 10^(-3) J`
D. `4.9 xx 10^(-5)J`

Answer

A

Explanation

Let the velocity of centre of sphere be `v`
The angular speed of a sphere about its centre is given by
`omega = (v)/(r)`
where, r = radius of sphere
The total kinetic energy = translational kinetic energy + rotational kinetic energy
`=(1)/(2)Iomega^(2)+(1)/(2)Mv^(2)=(1)/(2).(2)/(5)Mr^(2)omega^(2)+(1)/(2)Mv^(2)`
`=(1)/(5)Mv^(2)+(1)/(2)Mv^(2)=(7)/(10)Mv^(2)=(7)/(10)xx(1)/(2)xx(0.02)^(2)=1.4 xx10^(-4)J`.