• # question_answer DIRECTION: Read the passage given below and answer the questions that follows: In a thermally insulated tube of cross sectional area $\frac{GMm}{2R}$ a liquid of thermal expansion coefficient ${{10}^{-3}}\,{{K}^{-1}}$ is flowing. Its velocity at the entrance is $0.1\text{ }m/s$. At the middle of the tube a heater of a power of 10kW is heating the liquid. The specific heat capacity of the liquid is 1.5 kJ/(kg K), and its density is $1500\text{ }kg/{{m}^{3}}$ at the entrance. What is the density of liquid at the exit? A) 1450 kg/m3                    B) 1400 kg/m3    C) 1350 kg/m3    D) None of these

 ${{\text{ }\!\!\rho\!\!\text{ }}_{1}}{{v}_{1}}{{A}_{1}}={{\text{ }\!\!\rho\!\!\text{ }}_{2}}{{v}_{2}}{{A}_{2}}$ $\text{m =1500 kg/}{{\text{m}}^{\text{3}}}\text{ }\!\!\times\!\!\text{ 0}\text{.1m/s }\!\!\times\!\!\text{ 4}{{\left( \text{cm} \right)}^{\text{2}}}$ $ms\Delta T=10000$ $1500\times 0.1\times 4\times {{10}^{-4}}\times 1500\times \Delta T=10000$ $\Delta T=\frac{10000}{90}=\frac{1000}{9}{}^\circ C$ ${{\text{ }\!\!\rho\!\!\text{ }}_{\text{2}}}=\frac{{{\text{ }\!\!\rho\!\!\text{ }}_{\text{1}}}}{\left( 1+\text{ }\!\!\gamma\!\!\text{ }\Delta T \right)}=\frac{1500}{\left( 1+1\times {{10}^{3}}\times \frac{1000}{9} \right)}=1350kg/{{m}^{3}}$${{\text{ }\!\!\rho\!\!\text{ }}_{2}}{{v}_{2}}{{A}_{2}}={{\text{ }\!\!\rho\!\!\text{ }}_{1}}{{v}_{1}}{{A}_{1}}$ $\Rightarrow \,1350\times {{v}_{2}}=1500\times 0.1$ ${{v}_{2}}=1/9m/s$ $\therefore$Volume rate of flow at the end of tube $={{A}_{2}}{{v}_{2}}=4\times {{10}^{-4}}\times \frac{1}{9}$ $=\frac{4}{9}\times {{10}^{-4}}{{m}^{3}}=\frac{40}{9}\times {{10}^{-5}}{{m}^{3}}$ Volume rate of flow at the entrance = ${{A}_{1}}{{v}_{1}}$ $=0.1\times 4\times {{10}^{-4}}=4\times {{10}^{-5}}{{m}^{3}}$ Hence, difference of volume rate of flow at the two ends $=\left( \frac{40}{9}-4 \right)\times {{10}^{-5}}=\frac{4}{9}\times {{10}^{-5}}{{m}^{3}}$