Figure shows water in a container having `2.0mm` thick walls made of a material of thermal conductivity `0.50Wm^(-1).^(@)C^(-1)` . The container is kept in a melting-ice bath at `0^(@)C` . The total surface area in contact with water is `0.05m^(2)` . A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of `10cm^(-1)` and the temperature of the water remains constant at `1.0^(@)C` .Find the mass `M` of the block. Assume that the heat flow out of the water only through the walls in contact. Take `g=10ms^(-2)` .

Explanation

In steady state we use
`mgv=(kA)/(x)(T_(2)-T_(1))`
`M(10)(0.1)=(0.5xx0.05)/(2xx10^(-3))xx(l)`
`M=12.5 kg`