Question

A pan containing a layer of uniform thickness of ice is placed on a circular turn- table with its centre coinciding with the centre of the turn-table. The turn-table is now rotated at a constant angular velocity about a vertical axis passing through its centre and the driving torque is withdrawn. There is no friction between the table and the pivot. The pan rotates with the table. As the ice melts,

• A. the angular velocity of the system decreases
• B. the angular velocity of the system increases
• C. the angular velocity of the system remains unchanged
• D. the moment of inertia of the system increases

Answer 1

Answer: (A), (D)

the angular velocity of the system decreases
the moment of inertia of the system increases

$L_1=L_2$ (no external torque is present)
($\because$ net torque acting is zero )
$\therefore I_1{w}_1=I_2{w}_2$
(moment of inertia of the system (table +turn) will increase as the ice changes into water and move toward the end and always away from the axis)
$\therefore$ Angular velocity of the system will decrease