A body of moment of inertia about its axis of rotation is `3 kg m^(2)` and angular velocity 3 rad/s. The kinetic energy of rotating body is same as that of body of mass 27 kg moving with a speed of

Options

A. `1ms^(-1)`
B. `0.5ms^(-1)`
C. `2ms^(-1)`
D. `1.5ms^(-1)`

Answer

A

Explanation

We know that, the kinetic energy `=K=(1)/(2)mv^(2)=(1)/(2)l omega^(2)`
where, `m=27kg" (mass of the body)"`
`omega="3 rad s"^(-1)" (angular velocity)"`
`l=3"kg-m"^(2)v=?" (moment of inertia)"`
`"or "mv^(2)=lomega^(2)`
`v^(2)=(lomega^(2))/(m)=(3xx3^(2))/(27)=(27)/(27)=1`
`rArr" "v=sqrt1=1ms^(-1)`