A) 5 min
B) 10 min
C) 20 min
D) 80 min
Correct Answer: B
Solution :
| \[\text{Time}\propto \frac{1}{\text{Cross}-\text{Sectional}\,\,\text{area}\,\,\text{of}\,\,\text{the}\,\,\text{pipe}}\] |
| Time \[\propto \frac{1}{\frac{\pi }{4}{{d}^{2}}}\]\[\Rightarrow \]Time \[\propto \frac{1}{{{d}^{2}}}\] |
| \[\therefore \]\[\frac{{{t}_{2}}}{{{t}_{1}}}=\frac{{{({{d}_{1}})}^{2}}}{{{({{d}_{2}})}^{2}}}\]\[\Rightarrow \]\[{{t}_{2}}={{t}_{1}}{{\left( \frac{{{d}_{1}}}{{{d}_{2}}} \right)}^{2}}\] |
| \[{{t}_{2}}=40\,\,\min ,\]\[{{d}_{1}}=d,\]\[{{d}_{2}}=2d\] |
| \[\therefore \] \[{{t}_{2}}=40{{\left( \frac{d}{2d} \right)}^{2}}\]\[\Rightarrow \]\[{{t}_{2}}=40{{\left( \frac{1}{2} \right)}^{2}}\] |
| \[\therefore \] \[{{t}_{2}}=10\]min |
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