A body of moment of inertia of `3 kg m^(2)` rotating with an angular velocity of 2 rad/s has the same kinetic energy as that that of mass 12 kg moving with a velocity of

Options

A. `8ms^(-1)`
B. `0.5ms^(-1)`
C. `2ms^(-1)`
D. `1ms^(-1)`

Answer

D

Explanation

KE of rotation is given by, `KE_("rot")=(1)/(2)l omega^(2)`
As rotational KE = translational KE
`"So, "(1)/(2)l omega^(2)=(1)/(2)mv^(2)" or "mv^(2)=l omega^(2)`
`"or "v=omega sqrt(((l)/(m)))=2sqrt(((3)/(12)))=2xx(1)/(2)=1ms^(-1)`