A circular table rotates about a vertical axis with a constant angular speed w. A circular pan rests on the turn table (with the center of table)and rotates with the table.The bottom of the pan is covered with a uniform thick layer of ice which also rotates with the pan.The ice starts melting.The angular speed of the turn table

a)remains the same b)decreases c)increases d)none.

Dear student,

Applying conservation of linear and angular momentum. the angular speed of turn table remains same.

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

since there is no external torque acting on the system so angular momentam will remain conserved...

IW = constant    or

IW = I_fW_f          ..........1           (I_f , W_f are moment of inertia & angular velocity of final state)

initially ice was at center and contribution of  mass of ice  for inertia is 0...

I_ice = mr²     =0            (at center ,r=0)

finally ice melts & spreads over the turntable now its different small small elements contribute moment of inertia & net moment of inertia of system is somewhat more than initial value...

final moment of inertia = I+I_ice

from eq 1

IW = (I+I₁)W_f

 W_f  < W

hence option b) is correct

due to increase in moment of inertia ,angular velocity of table decreases ...

option b) is correct