A body having a moment of inertia about its axis of rotation equal to 3 kg `m^(-2)` is rotating with angular velocity of 3 rad `s^(-1)`. Kinetic energy of this rotating body is same as that of a body of mass 27 kg moving with velocity v. The value of v is

Options

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

Answer

A

Explanation

K.E. of rotating body is `E_("rot")`
`=(1)/(2)Iomega^(2)=(1)/(2)xx3xx3^(2)=(27)/(2)J`
K.E. of body of mass m moving with speed v is
`E=(1)/(2)mv^(2)=(1)/(2)xx27xxv^(2)`
A.T.P `(1)/(2)xx27xxv^(2)=(27)/(2)impliesv=1ms^(-1)`