A kathak dancer is standing on horizontal surface with folded hands. In the begining dancer is rotating about his central axis and his kinetic energy is 'K' at that time. The kathak dancer now stretches his arms so that the moment of inertia of the dancer becomes three times and the angular velocity becomes one-third. The kinetic energy of the dancer now is

Step-by-step solution

Initial kinetic energy of the dancer is given by K = 1 2 I ^2 When the dancer stretches his arms, the new moment of inertia becomes I' = 3I and the new angular velocity becomes ' = 3 The new kinetic energy is K' = 1 2 I' '^2 Substituting the values of I' and ' : K' = 1 2 (3I) ( 3 )^2 K' = 1 2 (3I) ( ^2 9 ) K' = 1 3 ( 1 2 I ^2 ) K' = K 3 Answer: K 3