The transfer of heat between the bottom surface of the beaker and water inside it is due to Convection phenomenon. When a fluid, such as air or a liquid, is heated and then travels away from the source, it carries the thermal energy along. ... The fluid above a hot surface expands, becomes less dense, and rises
The heat released by the water when it cools down by a temperature difference

is

where
m=432 g is the mass of the water

is the specific heat capacity of water

is the decrease of temperature of the water
Plugging the numbers into the equation, we find

and this is the amount of heat released by the water.
(a) 1200 rad/s
The angular acceleration of the rotor is given by:

where we have
is the angular acceleration (negative since the rotor is slowing down)
is the final angular speed
is the initial angular speed
t = 10.0 s is the time interval
Solving for
, we find the final angular speed after 10.0 s:

(b) 25 s
We can calculate the time needed for the rotor to come to rest, by using again the same formula:

If we re-arrange it for t, we get:

where here we have
is the initial angular speed
is the final angular speed
is the angular acceleration
Solving the equation,

I think its Mercury because it's the closest to the sun.