question_answer

Water is flowing continuously from a tap having an internal diameter \[8\times {{10}^{-3}}m\]. The water velocity as it leaves the tap is \[0.4\,m{{s}^{-1}}\]. The diameter of the water stream at a distance \[2\times {{10}^{-1}}m\] below the tap is close to   AIEEE  Solved  Paper-2011

A) \[3.6\times {{10}^{-3}}m\]                             

B) \[5.0\times {{10}^{-3}}m\]

C) \[7.5\times {{10}^{-3}}m\]                             

D) \[9.6\times {{10}^{-3}}m\]

Correct Answer: A

Solution :

             \[{{a}_{1}}{{v}_{1}}={{a}_{2}}{{v}_{2}}\] \[{{v}_{2}}^{2}={{v}_{1}}^{2}+2gh\] \[{{v}_{2}}^{2}={{(0.4)}^{2}}+2\times 10\times 0.2\]    \[={{(0.4)}^{2}}+4\] \[{{v}_{2}}^{2}=4.61\]              \[{{v}_{2}}=\sqrt{4.16}\] \[{{v}_{2}}=2.04\,m/s\] Also, \[{{a}_{1}},{{V}_{1}}={{a}_{2}}{{V}_{2}}\] \[{{d}_{1}}^{2}{{V}_{1}}={{d}_{2}}^{2}{{V}_{2}}\] \[{{d}_{2}}={{d}_{1}}\sqrt{\frac{{{V}_{1}}}{{{V}_{2}}}}\] \[=8\times {{10}^{-3}}\sqrt{\frac{0.4}{2.04}}\]  \[=3.54\times {{10}^{-3}}m\]