A body having a moment of inertia about its axis of rotation equal to 3 "kg-m"^(3) 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 a velocity v. The value of v is

A body having a moment of inertia about its axis of rotation equal to

1.	A body having a moment of inertia about its axis of rotation equal to 3 "kg-m"^(3) 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 a velocity v. The value of v is
Answer» `1 ms^(-1)` `0.5 ms^(-1)` `2 ms^(-1)` `1.5 ms^(-1)` Solution :We know that the kinetic energy, `K = (1)/(2)mv^(2)=(1)/(2)I omega^(2)` where, `m = 27 kg` (mass of the BODY) `omega = 3 "rads"^(-1)` (angular VELOCITY) `I = 3 "kg-m"^(2)` (moment of INERTIA) `v = ? or mv^(2)=I omega^(2)` `rArr v^(2)=(I omega^(2))/(m)rArrv^(2)=(3xx3^(2))/(27)rArrv^(2)=(27)/(27)=1` `rArr` Velocity of body, `v = sqrt(1) = 1 ms^(-1)`.