Solving Two Physics Questions: Rotational Inertia & Equilibrium Temp.

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The discussion revolves around solving two physics problems involving an Atwood's machine and thermal equilibrium. The first problem requires calculating the rotational inertia of a pulley connected to two masses, with the solution yielding 0.0546. The second problem involves determining the equilibrium temperature after dropping ice cubes into warmer water, with incorrect calculations suggesting 0 degrees Celsius. The correct equilibrium temperature options provided are 1.41° C, 2.82° C, 5.64° C, and 11.3° C. Assistance is requested for detailed solutions to both questions.
anuragpapineni
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Two masses, 300 g and 400 g, are connected by a cord that passes over a pulley with a radius of 6.64 cm (an Atwood's machine). When released from rest, the 400-g mass falls 60 cm and the 300-g mass rises 60 cm in 4.00 seconds. Find the rotational inertia of the pulley.

Four 100-g ice cubes at a temperature of -20° C are dropped into an insulated cup containing 800 g of water at a temperature of 44° C. Find the equilibrium temperature of the mixture.

These two questions were on a recent competition I was at. The first one had an answer of 0.0546 but I'm not sure how I got there. For the second I kept getting 0 degrees Celsius which was wrong. The other answer choices were
B. 1.41° C
C. 2.82° C
D. 5.64° C
E. 11.3° C

help solving either is appreciated
 
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Please post your working for each.
 
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