Two men of equal masses stand at opposite ends of the diameter of a turntable disc of a certain mass. Moving with constant angular velocity. The two men make their way to the middle of the turntable at equal rates in doing so

Options

A. kinetic energy of rotation has increased while angular momentum remains same
B. kinetic energy of rotation has decreased while angular momentum remains same
C. kinetic energy of rotation has decreased but angular momentum has increased
D. both, kinetic energy of rotation and angular momentum have decreased

Answer

A

Explanation

`I_(1)omega_(1) = I_(2) omega_(2)`
Since, men move towards middle of turm table `I_(2)` decrease hence `omega_(2)` increase.
`:. Delta K = I_(1)omega_(1)^(2) - (1)/(2) I_(2) omega_(2)^(2)`
`= (1)/(2) I_(1)omega_(1)^(2) [1 - (I_(2))/(I_(1)).(omega_(2)^(2))/(omega_(1)^(2))]`
`{(omega_(2))/(omega_(1)) gt 1 }`
`= (1)/(2) I_(1)omega_(1)^(2) [1 - (omega_(2))/(omega_(1))] lt 0`
So kinetic energy increases.