Figure shows water in a container having `2.0-mm` 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 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 `10cms^(-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)` .

Answer

A, B

Explanation

Given, `theta_(1)=1^(@)C,(theta_(2))=0^(@)C`
`K=0.5W//m-^(@)C, d=2mm`
`=2xx10^(3)m`
`A=5xx10^(-2) m^(2),`
`Q=10 cm//s=0.1 m//s`
Power =force xx Velocity
`mg xx (theta)`
Again, Power =(dQ)/(dt)=(KA(theta_(1)=theta_(2))/d`
` so, mgQ=(KA(theta_(1)=theta_(2))/d`
`m=(KA(theta_(1)=theta_(2))/(dQg)`
`(5xx10^_(1)xx5xx10_(-2)x1)/(2xx10^(-3)xx10^(-1)xx10)`
`=(25/2)=12.5kg.`