Q.

Figure shows a paddle wheel coupled with an agitator submerged in a water tank placed in an ice bath. The thickness of tank walls is 2mm and with thermal conductivity 0.5W/m∘C. The surface area of tank in contact with water is 0.05m2. As the block of mass M attached to wheel goes down agitator rotates. It is found that in steady state block goes down at a constant speed of 0.1m/s and water temperature remain constant at 1°C. Find the mass of block (in kg).  (Take g=10m/s2 )

Moderate

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a

14.5

b

16.5

c

12.5

d

11.5

answer is 3.

(Detailed Solution Below)

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Detailed Solution

rate of loss in gravitational  potential energy of block is equal to the rate of heat conduction from water to ice bath as Twater =constant.rate of loss of gravitational P.E. is = Mg vrate of the thermal conduction dθdt=kAT2−T1x=0.5×0.05×12×10−3=12.5 Js.for steady temperature of water           Mg ⁡v=12.5                                              M=12.510×0.1=12.5kg
ctaimg
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